Constraint-Safe Graph-Context Scoring for Stable Point-Feature Labels Under Text-Width and Accessibility-Inspired Profiles

# Constraint-Safe Graph-Context Scoring for Stable Point-Feature Labels Under Text-Width and Accessibility-Inspired Profiles
Source: [https://arxiv.org/html/2609.19848](https://arxiv.org/html/2609.19848)
###### Abstract

Point\-feature label placement on interactive maps must reconcile geometric validity, display yield, local placement utility, and stability across camera motion\. Accessibility and multilingual requirements further change label dimensions, yet algorithmic evaluations often collapse these concerns into overlap counts\. We present LABELSENSE\-Pilot, a reproducible prototype that generates eight compass candidates per feature, scores candidates with a multilayer perceptron over graph\-context summaries, adds a previous\-placement bonus, and selects a layout through mixed\-integer optimization\. The executed scorer is deliberately not described as a graph transformer\. Every returned layout is checked for viewport containment, per\-feature uniqueness, and pairwise clearance\. Experiments use 2,500 airport coordinates and names spanning 155 countries, with country\-grouped splits and generated density, camera, text\-suffix, preference, and enlarged\-font stressors\. Across five seeds, LABELSENSE\-Pilot displayed 85\.62 percent of labels with 2\.09 percent flicker and zero collisions\. Versus a handcrafted\-utility integer program, LABELSENSE\-Pilot sacrificed 1\.43 percentage points of display while reducing flicker by 12\.04 points\. Enlarged\-box\-aware layouts produced zero proxy violations, whereas standard geometry reevaluated at 1\.5x violated 52\.57 percent of selected placements\. These results establish an auditable engineering trade\-off, not human accessibility, multilingual usability, or preference\. Official recent baselines and participant evidence remain required before submission\.

###### Index Terms:

map labeling, point\-feature labeling, temporal stability, constrained optimization, graph context, accessibility proxy, multilingual text

## IIntroduction

Placing text near point features is deceptively difficult\. A label should remain inside the viewport, avoid every other selected label, stay close to its anchor, respect feature priority, and use a position that readers can associate with the point\. On an interactive map, the solution also has memory: a layout that is geometrically valid in every frame may still be difficult to follow when positions switch after small pans or zooms\. Label width changes under localization and font enlargement make the feasible set itself dependent on the rendering profile\. These coupled effects motivate a placement system that separates inviolable geometry from configurable utility\.

Point\-feature labeling has long been formulated through finite candidate positions, conflict graphs, heuristics, and combinatorial optimization\[[1](https://arxiv.org/html/2609.19848#bib.bib30),[2](https://arxiv.org/html/2609.19848#bib.bib10),[3](https://arxiv.org/html/2609.19848#bib.bib11),[4](https://arxiv.org/html/2609.19848#bib.bib32),[5](https://arxiv.org/html/2609.19848#bib.bib31),[6](https://arxiv.org/html/2609.19848#bib.bib33),[7](https://arxiv.org/html/2609.19848#bib.bib6)\]\. Recent work adds reinforcement learning for map labels\[[8](https://arxiv.org/html/2609.19848#bib.bib3)\], graph\-based learning in the adjacent illustration\-labeling domain\[[9](https://arxiv.org/html/2609.19848#bib.bib2)\], explicit preference evidence\[[10](https://arxiv.org/html/2609.19848#bib.bib22)\], and temporal consistency\[[11](https://arxiv.org/html/2609.19848#bib.bib18),[12](https://arxiv.org/html/2609.19848#bib.bib34),[13](https://arxiv.org/html/2609.19848#bib.bib35),[14](https://arxiv.org/html/2609.19848#bib.bib12)\]\. Accessibility research also makes clear that readable web maps require more than collision avoidance\[[15](https://arxiv.org/html/2609.19848#bib.bib25),[16](https://arxiv.org/html/2609.19848#bib.bib36),[17](https://arxiv.org/html/2609.19848#bib.bib37),[18](https://arxiv.org/html/2609.19848#bib.bib28)\]\. A single system that claims to unify all these strands therefore carries an unusually high evidence burden\. In particular, a geometry check cannot stand in for a study with low\-vision readers, and a few script\-bearing strings cannot establish multilingual usability\.

This paper reports a deliberately bounded algorithmic pilot\. LABELSENSE\-Pilot generates eight axis\-aligned candidate rectangles, represents local competition with three fixed graph\-context summaries, learns a candidate utility through a small multilayer perceptron \(MLP\), applies a previous\-direction bonus, and uses a binary mixed\-integer program \(MILP\) to enforce viewport and pairwise\-clearance constraints\. The implementation is not an end\-to\-end graph transformer\. Its preference targets, camera paths, density patterns, generic facility suffixes, and enlarged\-font profiles are generated stressors\. Real evidence is limited to the coordinates and source names of a pinned 2,500\-airport fixture\. These boundaries are part of the result rather than fine print\.

The pilot asks three engineering questions\. First, can learned graph\-context scoring plus exact feasibility display more labels than its learned greedy decoder? Second, does a temporal bonus reduce direction changes relative to independent\-frame scoring? Third, does constructing candidates at the evaluation font scale prevent enlarged\-box violations that an unaware layout incurs? The evaluation also records where the method loses: a handcrafted MILP displays slightly more labels, dynamic greedy is more stable, and both recent\-inspired greedy proxies are far faster\.

The contributions are:

- •An auditable hybrid architecture that combines fixed graph\-context features and an explicitly identified MLP surrogate with a hard\-constrained MILP decoder and an independent geometric audit\.
- •A reproducible five\-seed pilot with country\-grouped data splits, matched candidates, six local comparators, ten quantitative panels, synchronized result tables, and declared synthetic stressors for time, text width, preference, and enlarged geometry\.
- •A claim\-and\-submission gate that distinguishes collision\-free computation from human\-centered evidence and records the unexecuted graph\-transformer, official\-baseline, urban\-data, authentic\-translation, and participant\-study requirements\.

The remainder of this paper is organized as follows\. Section[II](https://arxiv.org/html/2609.19848#S2)positions the pilot against candidate\-based, learned, dynamic, preference, and accessibility research\. Section[III](https://arxiv.org/html/2609.19848#S3)defines the executed scoring and constrained decoder\. Section[IV](https://arxiv.org/html/2609.19848#S4)reports the protocol and results\. Section[V](https://arxiv.org/html/2609.19848#S5)interprets the trade\-offs, threats, and submission gate, and Section[VI](https://arxiv.org/html/2609.19848#S6)concludes\.

## IIRelated Work

### II\-ACandidate\-Based and Learned Placement

The classical point\-feature problem selects at most one candidate from a finite set for each point\. Its conflict graph exposes incompatible rectangles, while position, anchor distance, and feature priority define soft value\. Early empirical work compared greedy, gradient\-descent, and simulated\-annealing strategies\[[1](https://arxiv.org/html/2609.19848#bib.bib30)\]\. Exact formulations include large 0–1 cartographic programs, optimal rectangular\-label models, and extended integer programs beyond a plain maximum independent set\[[2](https://arxiv.org/html/2609.19848#bib.bib10),[3](https://arxiv.org/html/2609.19848#bib.bib11),[7](https://arxiv.org/html/2609.19848#bib.bib6)\]\. Recent parallel and spatial\-pattern methods broaden the scale–quality trade space through map segmentation, fixed–sliding hybrids, and data\-mined placement order\[[19](https://arxiv.org/html/2609.19848#bib.bib8),[20](https://arxiv.org/html/2609.19848#bib.bib9),[21](https://arxiv.org/html/2609.19848#bib.bib7)\]; GPU\-parallel greedy evaluation targets interactive throughput\[[22](https://arxiv.org/html/2609.19848#bib.bib5)\]\. Our decoder remains in this established finite\-candidate family\. “Exact” refers to the encoded constraints of a returned, independently checked incumbent, not polynomial runtime or a universal cartographic optimum\.

Learned systems can model interactions omitted by handcrafted scores\. Reinforced Labels applies multi\-agent deep reinforcement learning to point\-feature placement\[[8](https://arxiv.org/html/2609.19848#bib.bib3)\]\. LPGT and its retrieval\-augmented LPCE successor learn interactions for appliance\-manual illustrations, not maps\[[9](https://arxiv.org/html/2609.19848#bib.bib2),[23](https://arxiv.org/html/2609.19848#bib.bib1)\]\. RL\-LABEL addresses dynamic augmented\-reality labels\[[24](https://arxiv.org/html/2609.19848#bib.bib4)\]\. These adjacent architectures motivate context\-sensitive scoring, but the executed model here is materially smaller: three deterministic neighborhood summaries feed a conventional two\-hidden\-layer MLP\. It neither reproduces those systems nor substantiates a transformer claim\.

### II\-BTemporal Consistency

Dynamic\-map research distinguishes per\-frame validity from sequence quality\. Foundational work formulated consistent pan/zoom labeling and optimized active ranges\[[25](https://arxiv.org/html/2609.19848#bib.bib20),[26](https://arxiv.org/html/2609.19848#bib.bib29)\]\. A later experimental framework and its journal development formalized temporal intervals and algorithms\[[27](https://arxiv.org/html/2609.19848#bib.bib19),[11](https://arxiv.org/html/2609.19848#bib.bib18)\]; they form a related version family rather than two independent novelty signals\. Hybrid optimization addresses smoothness\[[28](https://arxiv.org/html/2609.19848#bib.bib15)\], transition research studies changing point\-label geometry\[[29](https://arxiv.org/html/2609.19848#bib.bib14)\], and fully dynamic independent\-set work handles evolving conflict graphs\[[30](https://arxiv.org/html/2609.19848#bib.bib16)\]\. Recent methods target fixed\-scale dense exploration, zoom\-aware tabu search, and time\-slider consistency\[[31](https://arxiv.org/html/2609.19848#bib.bib17),[32](https://arxiv.org/html/2609.19848#bib.bib13),[14](https://arxiv.org/html/2609.19848#bib.bib12)\]\. LABELSENSE\-Pilot uses only the previous compass direction\. It therefore tests short\-horizon switching on scripted motion, not global temporal consistency, transitions, or observed interaction behavior\.

### II\-CPreference, Language, and Accessibility

Placement preference is not interchangeable with a conventional top\-right rule\. Scheuerman*et al\.*published explicit binary and ranking judgments plus a companion data record\[[10](https://arxiv.org/html/2609.19848#bib.bib22),[33](https://arxiv.org/html/2609.19848#bib.bib21)\]\. The current execution did not acquire those responses and instead uses three disclosed synthetic rankings\. Production audits show that authentic label geometry and association remain practical cartographic challenges\[[34](https://arxiv.org/html/2609.19848#bib.bib23)\]\. Our five suffix conditions exercise only a character\-class width heuristic; they do not implement browser shaping, validated translation, bidirectionality, or font fallback\.

Accessibility work covers typography, contrast, interaction, adaptation, and nonvisual exploration\. Large\-print SVG maps and general accessible\-web\-map recommendations predate this pilot\[[35](https://arxiv.org/html/2609.19848#bib.bib27),[18](https://arxiv.org/html/2609.19848#bib.bib28)\]; AltGeoViz supports accessible geovisualization\[[36](https://arxiv.org/html/2609.19848#bib.bib26)\]; recent indoor\-map adaptations and thematic\-web\-map criteria add disabled\-community and low\-vision perspectives\[[37](https://arxiv.org/html/2609.19848#bib.bib24),[15](https://arxiv.org/html/2609.19848#bib.bib25)\]\. Enlarging rectangles and auditing overlap is consequently only an accessibility\-inspired geometry proxy\. It does not measure readability, comprehension, error, or task performance\.

Table[I](https://arxiv.org/html/2609.19848#S2.T1)summarizes the nearest capabilities conservatively\. A check mark denotes evidence in the cited setting, not matched semantics or an official reproduction\. The final row records what this artifact actually executes\.

TABLE I:Closest\-work capability matrix\. “Hard” denotes explicit feasibility constraints; “human” denotes participant\-derived evidence\. Proxy outcomes do not qualify as human evidence\.The defensible gap is narrower than the aspirational concept\. This pilot contributes a transparent integration of learned local utility, one\-step persistence, profile\-dependent rectangles, and constraint\-safe decoding under a reproducible protocol\. It does not establish the novelty or benefit of a graph transformer, real preference learning, authentic multilingual layout, or accessible map use; those remain conditional extensions requiring direct evidence\.

## IIIMethod

### III\-AProblem and Notation

At framett, featurei∈ℐti\\in\\mathcal\{I\}\_\{t\}has screen anchorai​t=\(xi​t,yi​t\)a\_\{it\}=\(x\_\{it\},y\_\{it\}\), source namesis\_\{i\}, prioritypi∈\[0,1\]p\_\{i\}\\in\[0,1\], and optionally a compass direction selected att−1t\-1\. The viewport isV=\[0,W\]×\[0,H\]V=\[0,W\]\\times\[0,H\]withW=1024W=1024andH=768H=768in the experiments\. Each point receives the eight compass candidates𝒦=\{N,N​E,E,S​E,S,S​W,W,N​W\}\\mathcal\{K\}=\\\{N,NE,E,SE,S,SW,W,NW\\\}plus implicit non\-display\. Table[II](https://arxiv.org/html/2609.19848#S3.T2)gives the principal symbols\.

TABLE II:Notation for the executed pilot\.The suffix conditionggappends a controlled facility term while preserving the proper\-name stem\. A character\-class functionω⁡\(c\)\\omega\(c\)assigns 0\.33 units to spaces, 1\.00 to CJK characters, 0\.68 to Arabic characters, 0\.85 to selected wide Latin symbols, 0\.32 to narrow symbols, and 0\.58 otherwise\. With font sizeffand enlargement factorα\\alpha, the heuristic dimensions are

q⁡\(si,g\)\\displaystyle q\(s\_\{i\},g\)=max⁡\(1,∑c∈si⊕gω⁡\(c\)\),\\displaystyle=\\max\\\!\\left\(1,\\sum\_\{c\\in s\_\{i\}\\oplus g\}\\omega\(c\)\\right\),\(1\)\(wi,hi\)\\displaystyle\(w\_\{i\},h\_\{i\}\)=\(q​α​f\+8,1\.35​α​f\+4\)\.\\displaystyle=\(q\\alpha f\+8,1\.35\\alpha f\+4\)\.This is deterministic width stress; it is not glyph shaping, translation validation, or a perceptual accessibility model\.

For directionkk, let\(dxk,dyk\)∈\{−1,0,1\}2\(d\_\{x\}^\{k\},d\_\{y\}^\{k\}\)\\in\\\{\-1,0,1\\\}^\{2\}be its unit compass offset ando=4o=4pixels\. The candidate center and rectangle are

ci​k​t\\displaystyle c\_\{ikt\}=ai​t\+\(dxk​\(wi/2\+o\),dyk​\(hi/2\+o\)\),\\displaystyle=a\_\{it\}\+\\left\(d\_\{x\}^\{k\}\(w\_\{i\}/2\+o\),d\_\{y\}^\{k\}\(h\_\{i\}/2\+o\)\\right\),\(2\)Ri​k​t\\displaystyle R\_\{ikt\}=ci​k​t\+\[−wi/2,wi/2\]×\[−hi/2,hi/2\]\.\\displaystyle=c\_\{ikt\}\+\[\-w\_\{i\}/2,w\_\{i\}/2\]\\times\[\-h\_\{i\}/2,h\_\{i\}/2\]\.Viewport validity is precomputed as

Fi​k​t=𝟏​\{0≤R0x,R1x≤W,0≤R0y,R1y≤H\}\.F\_\{ikt\}=\\mathbf\{1\}\\\{0\\leq R^\{x\}\_\{0\},\\;R^\{x\}\_\{1\}\\leq W,\\;0\\leq R^\{y\}\_\{0\},\\;R^\{y\}\_\{1\}\\leq H\\\}\.\(3\)

### III\-BPreference and Graph\-Context Features

The three profiles \(balanced, right, and upper\) define complete, disclosed rankings of the eight directions\. Ifrπ​\(k\)∈\{0,…,7\}r\_\{\\pi\}\(k\)\\in\\\{0,\\ldots,7\\\}is the rank under profileπ\\pi, the proxy agreement feature is

Pπ​\(k\)=1−rπ​\(k\)7\.P\_\{\\pi\}\(k\)=1\-\\frac\{r\_\{\\pi\}\(k\)\}\{7\}\.\(4\)It is generated and should not be confused with the participant responses in\[[10](https://arxiv.org/html/2609.19848#bib.bib22),[33](https://arxiv.org/html/2609.19848#bib.bib21)\]\.

Graph context is computed over point anchors before candidate selection\. For every other pointjj, letdi​j=∥ai​t−aj​t∥2d\_\{ij\}=\\lVert a\_\{it\}\-a\_\{jt\}\\rVert\_\{2\}\. The three fixed summaries are

Li\\displaystyle L\_\{i\}=∑j≠ie−di​j/100w¯j∑j≠ie−di​j/100,\\displaystyle=\\frac\{\\sum\_\{j\\neq i\}e^\{\-d\_\{ij\}/100\}\\,\\bar\{w\}\_\{j\}\}\{\\sum\_\{j\\neq i\}e^\{\-d\_\{ij\}/100\}\},Qi\\displaystyle Q\_\{i\}=∑j≠ie−di​j/240\(0\.5\+pj\)pj∑j≠ie−di​j/240\(0\.5\+pj\),\\displaystyle=\\frac\{\\sum\_\{j\\neq i\}e^\{\-d\_\{ij\}/240\}\(0\.5\+p\_\{j\}\)p\_\{j\}\}\{\\sum\_\{j\\neq i\}e^\{\-d\_\{ij\}/240\}\(0\.5\+p\_\{j\}\)\},Mi\\displaystyle M\_\{i\}=1\|ℐt\|−1∑j≠ie−di​j/90,\\displaystyle=\\frac\{1\}\{\|\\mathcal\{I\}\_\{t\}\|\-1\}\\sum\_\{j\\neq i\}e^\{\-d\_\{ij\}/90\},\(5\)wherew¯j=min⁡\(wj/250,2\)\\bar\{w\}\_\{j\}=\\min\(w\_\{j\}/250,2\)\. These exponential averages are fixed attention\-like summaries; their scales are not trained\. Candidate features concatenate bias, priority, preference, normalized anchor distance, viewport\-edge clearance, 150\-pixel density, normalized width, scale, previous\-direction match, and\(Li,Qi,Mi\)\(L\_\{i\},Q\_\{i\},M\_\{i\}\):

hi​k​t=\[\\displaystyle h\_\{ikt\}=\[1,pi,Pπ​\(k\),d¯i​k​t,ei​k​t,ρi​t,\\displaystyle 1,p\_\{i\},P\_\{\\pi\}\(k\),\\bar\{d\}\_\{ikt\},e\_\{ikt\},\\rho\_\{it\},\(6\)w¯i,α,zi​k​t,Li,Qi,Mi\]𝖳\.\\displaystyle\\bar\{w\}\_\{i\},\\alpha,z\_\{ikt\},L\_\{i\},Q\_\{i\},M\_\{i\}\]^\{\\mathsf\{T\}\}\.
There is no human\-labeled utility target\. Training instead uses a declared seeded proxy that combines the same interpretable quantities with Gaussian noiseϵ∼𝒩⁡\(0,0\.122\)\\epsilon\\sim\\mathcal\{N\}\(0,0\.12^\{2\}\):

yi​k​tsyn=\\displaystyle y\_\{ikt\}^\{\\rm syn\}=\{\}2\.2​pi\+2\.4​Pπ​\(k\)−0\.75​d¯i​k​t\+0\.50​ei​k​t\\displaystyle 2\.2p\_\{i\}\+2\.4P\_\{\\pi\}\(k\)\-0\.75\\bar\{d\}\_\{ikt\}\+0\.50e\_\{ikt\}−1\.25​ρi​t−0\.70​Li\+0\.35​Qi−1\.10​Mi\\displaystyle\-1\.25\\rho\_\{it\}\-0\.70L\_\{i\}\+0\.35Q\_\{i\}\-1\.10M\_\{i\}\+0\.55​pi​Pπ​\(k\)−0\.45​w¯i​Mi\+ϵ\.\\displaystyle\+0\.55p\_\{i\}P\_\{\\pi\}\(k\)\-0\.45\\bar\{w\}\_\{i\}M\_\{i\}\+\\epsilon\.\(7\)Train countries produce eight scenes of 30, 35, or 40 points per seed under rotating suffix and profile settings, totaling 2,200 candidate examples\. Features are standardized using training meansμ\\muand scalesσ\\sigma\. The executedGraphContextMLPis a1212–2020–1010–11regressor withtanh\\tanhhidden activations, Adam optimization,ℓ2\\ell\_\{2\}coefficient 0\.02, early stopping, and a seeded 15% internal validation fraction:

h~i​k​t\\displaystyle\\widetilde\{h\}\_\{ikt\}=\(hi​k​t−μ\)⊘σ,\\displaystyle=\(h\_\{ikt\}\-\\mu\)\\oslash\\sigma,ri​k​t\(1\)\\displaystyle r^\{\(1\)\}\_\{ikt\}=tanh⁡\(b1\+W1​h~i​k​t\),\\displaystyle=\\tanh\(b\_\{1\}\+W\_\{1\}\\widetilde\{h\}\_\{ikt\}\),ri​k​t\(2\)\\displaystyle r^\{\(2\)\}\_\{ikt\}=tanh⁡\(b2\+W2​ri​k​t\(1\)\),\\displaystyle=\\tanh\(b\_\{2\}\+W\_\{2\}r^\{\(1\)\}\_\{ikt\}\),u^i​k​t\\displaystyle\\widehat\{u\}\_\{ikt\}=b3\+W3​ri​k​t\(2\)\.\\displaystyle=b\_\{3\}\+W\_\{3\}r^\{\(2\)\}\_\{ikt\}\.\(8\)
Fig\. 1:Executed frame pipeline\. Blue marks the only stage containing learned weights \(the MLP\); its graph summaries, box geometry, MILP constraints, and audit are deterministic\.
### III\-CTemporal Score and Constraint\-Safe Decoder

The one\-step state indicator equals one if objectiiretains directionkkfrom the preceding frame\. The final candidate utility is

ui​k​t\\displaystyle u\_\{ikt\}=u^i​k​t\+λT​zi​k​t,\\displaystyle=\\widehat\{u\}\_\{ikt\}\+\\lambda\_\{T\}z\_\{ikt\},\(9\)zi​k​t\\displaystyle z\_\{ikt\}=𝟏\{k=ki,t−1\},λT=1\.10\.\\displaystyle=\\mathbf\{1\}\\\{k=k\_\{i,t\-1\}\\\},\\qquad\\lambda\_\{T\}=1\.10\.The indicator rewards direction persistence; it does not penalize screen displacement after the known camera transform and it has no memory beyond one frame\.

For each candidate, invalid viewport geometry is disabled by

0≤xi​k​t≤Fi​k​t,xi​k​t∈\{0,1\}\.0\\leq x\_\{ikt\}\\leq F\_\{ikt\},\\qquad x\_\{ikt\}\\in\\\{0,1\\\}\.\(10\)At most one position may be chosen for each feature:

∑k∈𝒦xi​k​t≤1∀i∈ℐt\.\\sum\_\{k\\in\\mathcal\{K\}\}x\_\{ikt\}\\leq 1\\qquad\\forall i\\in\\mathcal\{I\}\_\{t\}\.\(11\)LetEtE\_\{t\}contain candidate pairs from distinct features whose rectangles overlap after clearanceδ=4\\delta=4pixels\. Each conflict creates

xi​k​t\+xj​ℓ​t≤1∀\(\(i,k\),\(j,ℓ\)\)∈Et\.x\_\{ikt\}\+x\_\{j\\ell t\}\\leq 1\\qquad\\forall\\big\(\(i,k\),\(j,\\ell\)\\big\)\\in E\_\{t\}\.\(12\)The decoder solves the binary program

maxx\\displaystyle\\max\_\{x\}\\quad∑i∈ℐt∑k∈𝒦ui​k​t​xi​k​t\\displaystyle\\sum\_\{i\\in\\mathcal\{I\}\_\{t\}\}\\sum\_\{k\\in\\mathcal\{K\}\}u\_\{ikt\}x\_\{ikt\}s\.t\.Eqs\. \([10](https://arxiv.org/html/2609.19848#S3.E10)\)–\([12](https://arxiv.org/html/2609.19848#S3.E12)\)\.\\displaystyle\\text\{Eqs\.~\\eqref\{eq:bounds\}\-\-\\eqref\{eq:conflicts\}\}\.\(13\)SciPy’s HiGHS interface receives a 0\.50\-s time limit and zero requested relative gap\. If no incumbent exists, the implementation invokes a feasible greedy fallback and records that status\. Every selected incumbent is then audited independently\. All main and reported sweep MILPs in this execution terminated optimally; the method nevertheless makes no general polynomial\-time or global\-runtime claim\.

### III\-DComplexity and Guarantee Scope

Fornnvisible features and eight candidates each, feature construction computes ann×nn\\times nanchor\-distance matrix and therefore costsO⁡\(n2\)O\(n^\{2\}\)time and memory in this pilot\. Pairwise rectangle testing isO⁡\(\(8​n\)2\)O\(\(8n\)^\{2\}\)\. MILP solution is NP\-hard in the worst case\. These choices favor clarity and auditability at the evaluated scale rather than asymptotic novelty\. The returned layout has a direct, machine\-checked guarantee only for the encoded axis\-aligned rectangles, viewport, and clearance\. It does not guarantee perceptual association, readable contrast, language correctness, or accessibility\.

Algorithm 1Train graph\-context utility surrogate1:country\-grouped training records, seed

ss
2:initialize seeded generator; set suffixes and profiles

3:foreach of eight training scenesdo

4:generate eight candidates and

hi​k​th\_\{ikt\}per point

5:compute declared target

yi​k​tsyny\_\{ikt\}^\{\\rm syn\}by Eq\. \([7](https://arxiv.org/html/2609.19848#S3.E7)\)

6:endfor

7:fit the standardizer on training candidates

8:fit seeded MLP by Eq\. \([8](https://arxiv.org/html/2609.19848#S3.E8)\) with early stopping

9:returnfrozen standardizer, MLP, training RMSE, metadata

Algorithm 2Place and audit one frame1:anchors, strings, profile, previous directions

2:form rectangles by Eqs\. \([1](https://arxiv.org/html/2609.19848#S3.E1)\)–\([3](https://arxiv.org/html/2609.19848#S3.E3)\)

3:compute graph summaries and candidate features

4:predict utility and apply Eq\. \([9](https://arxiv.org/html/2609.19848#S3.E9)\)

5:enumerate inter\-feature conflict set

EtE\_\{t\}
6:solve Eq\. \([13](https://arxiv.org/html/2609.19848#S3.E13)\) within the recorded limit

7:ifno MILP incumbent existsthen

8:construct a feasible utility\-sorted greedy layout

9:endif

10:recompute viewport, uniqueness, and clearance checks

11:returnselected directions, timings, status, audit metrics

## IVExperimental Evaluation

### IV\-AQuestions and Protocol

The executed study tests three prespecified engineering hypotheses: LABELSENSE\-Pilot should display more labels than the learned greedy decoder while preserving the encoded constraints \(H1\); the temporal term should reduce switching versus its removal \(H2\); and geometry\-aware optimization should avoid enlarged\-box violations that appear when 1\.0×\\timeslayouts are evaluated at 1\.5×\\timesgeometry \(H3\)\. None concerns human task performance\.

TABLE III:Executed point\-feature fixture and split\. Coordinates and source names are real; camera motion, language suffixes, preference targets, and accessibility profiles are synthetic stressors\.The bundled fixture contains 2,500 unique airport records from 155 countries\. Coordinates and source names are real; source rows identify OurAirports and are distributed in an OpenFlights\-format file\. The artifact records both providers’ source pages and licensing notes\. A deterministic country hash assigns 1,606 points to training, 292 to validation, and 602 to test, preventing points from one country appearing across splits\. The main evaluation uses scenes from Brazil, Finland, Iran, Mexico, and Sweden\. Airport points are not a substitute for dense urban OSM features; density sweeps replicate and jitter held\-out points after splitting\.

Five seeds \(7, 19, 31, 43, 61\) define one 42\-point, five\-frame sequence each\. The main comparison therefore contains 30 method–seed sequences and 150 frames\. All methods receive identical anchors, eight candidates, 12\-pixel base font, 1\.25×\\timesgeometry, profile, and four\-pixel clearance\. The MLP is trained anew for each seed using training countries only\. Its 2,200 synthetic targets per seed yield RMSEs from 0\.120 to 0\.124; this measures fit to the constructed target, not preference validity\.

We compare Onion\-Greedy; feasible 700\-iteration simulated annealing \(SimAnneal\); an exact decoder over handcrafted utility \(ILP\-Utility\); learned\-utility greedy selection \(GraphGreedy\-Reimpl\); learned greedy selection with previous\-direction hysteresis \(DynHysteresis\-Reimpl\); and LABELSENSE\-Pilot\. The two names ending in Reimpl are project\-local, recent\-inspired proxies\. An official recent implementation was not executed\. They are not LPGT, a faithful dynamic\-labeling reproduction, or evidence of parity with the corresponding publications\. This missing comparison is a submission blocker\.

Metrics are displayed labels divided by input points, pairwise collision count, mean anchor distance, synthetic preference agreement, frame\-to\-frame direction changes among labels visible in both frames \(flicker\), enlarged\-box violations, and single\-process wall time\. An initial frame has zero defined switching by construction\. Runtime includes candidate scoring and selection as recorded by the local method call but excludes data preparation and rendering\. All quantitative claims below are generated from CSV outputs rather than transcribed manually\.

### IV\-BMain Trade\-Off

TABLE IV:Main five\-seed pilot comparison\. Display, flicker, and preference are percentages; runtime is milliseconds per frame\. All methods produced zero counted geometric collisions under the supplied boxes\. Bold and underline denote best and second best only within this local execution\.Table[IV](https://arxiv.org/html/2609.19848#S4.T4)and Fig\.[2](https://arxiv.org/html/2609.19848#S4.F2)show a mixed outcome\. LABELSENSE\-Pilot displays 85\.62% of labels, with 2\.09% flicker, 76\.47% synthetic preference agreement, and 27\.01 ms per frame\. Every main method has a 100% collision\-free rate under the supplied rectangles and clearance\. ILP\-Utility displays the most labels \(87\.05%\) but switches positions on 14\.13% of shared selections\. Relative to that exact\-handcrafted comparator, LABELSENSE\-Pilot loses 1\.43 display percentage points, reduces flicker by 12\.04 points \(85\.2% relative\), and gains 2\.77 points on the synthetic preference metric\.

OnionSAILPGraphGDynHLS002020404060608080100100Rate \(%\)\(a\) Displayed labelsOnionSAILPGraphGDynHLS0010102020Changes \(%\)\(b\) Temporal flickerFig\. 2:Main five\-seed trade\-off\. Rates aggregate 25 frames per method; all displayed layouts had zero counted collisions\.The greedy learned comparators reveal the cost of constrained yield\. GraphGreedy\-Reimpl is approximately 61\.4×\\timesfaster and achieves higher synthetic preference agreement, but LABELSENSE\-Pilot displays 17\.24 additional percentage points\. DynHysteresis\-Reimpl has the lowest flicker at 0\.48%, yet displays only 68\.67% of input labels\. The proposed pilot therefore occupies a high\-yield, low\-switching region; it is not uniformly dominant\.

TABLE V:Paired exploratory contrasts across five generated\-scene seeds\. Differences are percentage points \(LABELSENSE\-Pilot minus comparator\); confidence intervals are paired bootstrap intervals\. Holm\-adjusted Wilcoxon values are descriptive becausen=5n=5\.Exploratory paired analyses average each five\-frame sequence within seed\. We report paired mean differences, 20,000\-sample bootstrap intervals, exact two\-sided Wilcoxon tests when defined, and Holm correction across the generated contrasts\. Table[V](https://arxiv.org/html/2609.19848#S4.T5)gives the three central comparator sets\. Every adjusted value is 1\.000\. Withn=5n=5constructed scene seeds, these values are descriptive consistency checks, not population inference or evidence of statistical equivalence\.

### IV\-CMotion, Text Width, Density, and Runtime

Figure[3](https://arxiv.org/html/2609.19848#S4.F3)separates camera amplitude from string length\. With no motion, position consistency is 100%; at 10% scripted amplitude it remains 93\.97%\. This behavior reflects one\-step direction reuse on a deterministic camera path and cannot predict stability under real interaction traces\. Increasing the length factor from 0\.75 to 1\.50 reduces displayed yield from 91\.00% to 70\.50%; the 1\.75 condition produces the same constructed string length for this generator and therefore repeats 70\.50%\.

005510108080858590909595100100Motion amplitude \(%\)Consistency \(%\)\(a\) Pan/zoom stability111\.51\.560608080100100Length factorDisplayed \(%\)\(b\) Label lengthFig\. 3:Controlled dynamic and text\-length sensitivity for LABELSENSE\-Pilot\. Camera motion is scripted and length factors alter generated strings\.Density exposes the binary solver cost \(Fig\.[4](https://arxiv.org/html/2609.19848#S4.F4)\)\. Display rate falls from 97\.00% at 20 points to 56\.25% at 80 as rectangular conflicts increase\. Mean local solver time grows from 7\.39 to 305\.96 ms\. All five 80\-point runs returned HiGHS\-optimal status within the configured 0\.50\-s limit, but the 163\.35\-ms standard deviation shows unstable tail behavior\. Because point distance and rectangle conflicts are both built quadratically, this pilot is not a production\-scale renderer\.

2020404060608080404060608080100100Features per viewportDisplayed \(%\)\(a\) Density202040406060808010110^\{1\}10210^\{2\}Features per viewportSolver time \(ms\)\(b\) RuntimeFig\. 4:Density scalability\. Runtime uses a log axis and reports the executed single\-process environment, not a hardware\-normalized benchmark\.
### IV\-DPreference, Suffix, and Enlarged\-Geometry Stress

Figure[5](https://arxiv.org/html/2609.19848#S4.F5)\(a\) repeats the main synthetic preference score to make its conflict with yield visible\. The learned greedy variants score highest because selection by the learned proxy can omit difficult labels\. The score is a mean over selected directions, so displaying fewer labels can make it easier to achieve a high value\. It must not be read as user preference\.

The suffix experiment appends generic facility terms in five scripts and estimates width through Eq\. \([1](https://arxiv.org/html/2609.19848#S3.E1)\)\. Display rates range from 83\.50% for the Spanish suffix to 89\.00% for the Japanese suffix \(Table[VI](https://arxiv.org/html/2609.19848#S4.T6)and Fig\.[5](https://arxiv.org/html/2609.19848#S4.F5)\(b\)\)\. This ordering follows constructed string widths and held\-out geometry; it is not evidence that one language performs better\. Source proper names were preserved, strings were not authenticated translations, and Arabic shaping, bidirectional layout, fallback fonts, truncation, and line breaking were not rendered\.

TABLE VI:Geometry stress results\. Suffix rows are controlled strings, not authenticated translations\.OnionSAILPGraphGDynHLS60608080100100Agreement \(%\)\(a\) Proxy preferenceendeesjaar6060707080809090100100Displayed \(%\)\(b\) Geometry stressFig\. 5:Synthetic preference and script\-suffix geometry stress\. Panel \(b\) is not a multilingual usability comparison\.The aware 1\.5×\\timesprofile constructs and optimizes enlarged rectangles, displays 79\.50%, and records 0\.00% post\-check violations\. The unaware GraphGreedy layout is optimized at 1\.0×\\timesand reevaluated at 1\.5×\\times; 52\.57% of its selected placements violate the enlarged\-box proxy\. This demonstrates geometry mismatch, not accessibility or low\-vision benefit\. A binary violation counts a viewport overflow or conflict event per selected layout convention and is not a participant outcome\.

### IV\-EAblation

TABLE VII:Component ablation \(percent\)\. Accessibility violations are enlarged\-box proxy violations\.Removing temporal utility raises flicker from 1\.61% to 12\.93%, a 11\.31\-point reduction for the full configuration, while display rate changes from 82\.50% to 82\.11%\. Removing the preference term drops synthetic agreement by 19\.39 points\. Replacing learned graph\-context scoring with handcrafted ILP raises display but also flicker and reduces the proxy score\. The unaware\-geometry variant displays 89\.08% at its smaller construction geometry, then incurs 66\.35% violations at 1\.5×\\timesevaluation\. Figure[6](https://arxiv.org/html/2609.19848#S4.F6)makes the yield–validity and yield–switching trade\-offs explicit\.

Aware 1xAware 1\.2xAware 1\.5xUnaware 1\.5x002020404060608080100100Rate \(%\)\(a\) Accessibility proxyDisplayedViolations5510106060707080809090100100Flicker \(%\)Displayed \(%\)\(b\) AblationFig\. 6:Accessibility\-inspired geometry stress and component ablation\. “Aware” means the solver used the evaluated box size; no participant accessibility outcome was collected\.H1–H3 pass only in their narrow engineering form: the proposed decoder displays more labels than learned greedy with audited geometric feasibility; its temporal term substantially reduces switching; and enlargement\-aware construction avoids the violations induced by mismatched boxes\. These outcomes do not validate the original graph\-transformer or human\-centered hypotheses\.

## VDiscussion

### V\-AWhat the Pilot Establishes

The results support one systems proposition: when every method shares a candidate set, a learned utility can be separated cleanly from a hard\-feasibility decoder\. The MILP never needs to trust the scorer about geometry; invalid candidates receive zero upper bounds and every conflict pair is constrained\. This separation permits preference and stability weights to change without weakening the encoded rectangle guarantee\. It also makes failure legible: a layout can be geometrically valid while scoring poorly, switching often, hiding too many labels, or failing a later enlarged\-box audit\.

The comparison with ILP\-Utility is especially informative\. The proposed scoring sacrifices only 1\.43 display points while cutting switching sharply, but that result is partly designed into the one\-step bonus\. It demonstrates that the implementation obeys its objective, not that people prefer the resulting sequence\. The even lower flicker of DynHysteresis\-Reimpl shows that a greedy persistence bias can be effective when lower display is acceptable\. A future interface should expose a Pareto frontier instead of claiming one universally best weight\.

The learned component also has a restricted interpretation\. The MLP predicts a synthetic target built from its own inputs, so low training RMSE confirms implementation consistency rather than discovery of latent cartographic taste\. The graph\-context terms are fixed radial averages\. They summarize competition but do not pass candidate\-level messages, learn attention weights, or model multiple layers of interaction\. Calling this implementation a graph transformer would therefore be inaccurate\.

### V\-BThreats to Validity

Construct validity\.Display and collision metrics concern axis\-aligned heuristic boxes\. They omit glyph outlines, halos, markers, leaders, color contrast, occlusion by map content, screen\-reader structure, and point–label ambiguity\. Synthetic preference agreement is conditional on displayed labels and may reward selective omission\. Flicker counts compass\-direction changes only among objects visible in consecutive frames; appearance, disappearance, and residual motion are not penalized\.

Data validity\.Airports differ materially from urban points of interest in density, naming, priority, and spatial pattern\. The pinned prefix is not a random global sample\. Dense scenes depend on replication and jitter\. Whole\-country splitting limits direct leakage but five held\-out countries do not establish cross\-region generalization\. Generic facility suffixes neither validate translation nor represent real localized map strings\.

Human and accessibility validity\.No participant was recruited, no human response file was analyzed, and no task\-completion time, comprehension, error, readability, or preference outcome was collected\. Enlarged\-font rectangles are an accessibility\-inspired geometry proxy only\. Passing the proxy does not establish WCAG conformance or accessible map use\[[15](https://arxiv.org/html/2609.19848#bib.bib25),[37](https://arxiv.org/html/2609.19848#bib.bib24)\]\. The identified preference dataset contains valuable prior responses, but it was not acquired in this run and would not substitute for multilingual and low\-vision validation\[[33](https://arxiv.org/html/2609.19848#bib.bib21)\]\.

Comparator validity\.Onion\-Greedy, SimAnneal, and ILP\-Utility are local implementations\. GraphGreedy\-Reimpl and DynHysteresis\-Reimpl capture broad scoring and hysteresis ideas but are not official recent systems\. No official LPGT, reinforced\-label, Rapid Labels, or temporal\-labeling code was executed\. Candidate sets, objectives, and hardware may differ from the cited literature, so the table supports only internal matched comparisons\.

Inference and performance validity\.Five generated\-scene seeds yield low\-powered paired summaries; Holm\-adjustedppvalues of 1\.000 preclude significance claims\. Bootstrap intervals describe these seeds, not a population\. Runtime was measured on one shared virtualized CPU with no renderer or network pipeline\. Means are not service\-level p95/p99 guarantees\.

## VIConclusion

LABELSENSE\-Pilot demonstrates an integration of graph\-context utility scoring, one\-frame temporal persistence, profile\-dependent label rectangles, and hard\-constrained point\-feature selection\. On five generated held\-out\-country sequences, the method displayed 85\.62 percent of labels, changed 2\.09 percent of shared placements, and produced no collisions under encoded boxes\. Compared with handcrafted MILP utility, it traded 1\.43 display percentage points for a 12\.04\-point flicker reduction\. Constructing labels at 1\.5 times font geometry avoided proxy violations, whereas layouts built at standard geometry and reevaluated after enlargement violated 52\.57 percent of selected placements\. These findings verify software behavior and expose yield, stability, preference\-proxy, and runtime trade\-offs\. They do not demonstrate accessible map use, multilingual usability, human preference, comprehension, or task performance\. The executed learner is an MLP over fixed graph\-context summaries, not a graph transformer; language strings, preference targets, density, and motion are generated stressors; and no official recent implementation was executed\. A publication\-ready study must add independent urban regions, authentic localized strings with pinned shaping, the intended graph model, official baselines, observed interaction traces, and preregistered participation by multilingual and low\-vision users\. Until those requirements are met and venue policies are rechecked, the Q1 submission decision remains NO\-GO\.

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