Skyline-First Traversal as a Control Mechanism for Multi-Criteria Graph Search
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arXiv
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| Format: | Preprint |
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2026
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| author | Tacheny, Nicolas |
| author_facet | Tacheny, Nicolas |
| contents | In multi-criteria graph traversal, paths are compared via Pareto dominance, an ordering that identifies which paths are non-dominated, but says nothing about which path to expand next or when the search may stop. As a result, existing approaches rely on external mechanisms-heuristics, scalarization, or population-based exploration while Pareto dominance remains confined to passive roles such as pruning or ranking.
This paper shows that, under constrained cost models, finite cost grids, Markovian transitions, and a nonzero progress measure, Pareto geometry alone is sufficient to drive both scheduling and termination. We show that extracting exclusively from the first Pareto layer, the skyline, induces a deterministic descent in a discrete completion potential, ensuring monotone progress toward solution completion. In parallel, a vector lower-bound certificate provides a stopping condition that guarantees dominance coverage of all remaining traversals without requiring a predefined number of solutions.
Our analysis establishes deterministic potential descent, certified termination via dominance coverage, a uniform bound on layer width induced by cost-grid geometry, and greedy cost-space dispersion within the skyline. The resulting framework operates without scalarization, heuristic guidance, or probabilistic models, and repositions Pareto dominance from a passive filter to a deterministic driver of search. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19807 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Skyline-First Traversal as a Control Mechanism for Multi-Criteria Graph Search Tacheny, Nicolas Artificial Intelligence Data Structures and Algorithms In multi-criteria graph traversal, paths are compared via Pareto dominance, an ordering that identifies which paths are non-dominated, but says nothing about which path to expand next or when the search may stop. As a result, existing approaches rely on external mechanisms-heuristics, scalarization, or population-based exploration while Pareto dominance remains confined to passive roles such as pruning or ranking. This paper shows that, under constrained cost models, finite cost grids, Markovian transitions, and a nonzero progress measure, Pareto geometry alone is sufficient to drive both scheduling and termination. We show that extracting exclusively from the first Pareto layer, the skyline, induces a deterministic descent in a discrete completion potential, ensuring monotone progress toward solution completion. In parallel, a vector lower-bound certificate provides a stopping condition that guarantees dominance coverage of all remaining traversals without requiring a predefined number of solutions. Our analysis establishes deterministic potential descent, certified termination via dominance coverage, a uniform bound on layer width induced by cost-grid geometry, and greedy cost-space dispersion within the skyline. The resulting framework operates without scalarization, heuristic guidance, or probabilistic models, and repositions Pareto dominance from a passive filter to a deterministic driver of search. |
| title | Skyline-First Traversal as a Control Mechanism for Multi-Criteria Graph Search |
| topic | Artificial Intelligence Data Structures and Algorithms |
| url | https://arxiv.org/abs/2604.19807 |