Skyline-First Traversal as a Control Mechanism for Multi-Criteria Graph Search

TL;DR

This paper introduces a novel control mechanism for multi-criteria graph search that leverages Pareto dominance and the skyline layer to guide traversal and termination without heuristics or scalarization.

Contribution

It demonstrates that Pareto geometry alone can deterministically drive scheduling and stopping criteria in multi-criteria graph search under specific models.

Findings

Finite cost grids and Markovian transitions enable deterministic descent.

Skyline layer extraction guarantees monotone progress toward solutions.

A vector lower-bound certificate ensures guaranteed termination.

Abstract

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.