arXiv AI

Key-Interval A*: Accelerating Grid Pathfinding via Structural Abstraction

arXiv:2607. 23393v1 Announce Type: new Abstract: Existing exact methods for 4-connected grid pathfinding reduce online search, but often either retain fine-grained search states or require substantial preprocessing.

arXiv AI
Aug 24

Unified Branch-and-Bound Search for the Steiner Traveling Salesman Problem on Graphs of Convex Sets

The paper introduces a unified branch‑and‑bound framework for the Steiner Traveling Salesman Problem on Graphs of Convex Sets (GCS), where the goal is to find a minimum‑cost closed walk through required convex sets while allowing optional vertices and revisits. The method uses additive lower‑bound graph costs for committed prefixes and a cut‑separated connected‑flow relaxation for the remaining cost, guaranteeing finite termination under a uniform positive‑cost assumption. Experiments on benchmark instances show that both best‑first and depth‑first traversal strategies find feasible solutions within 30 seconds, achieving mean certified optimality gaps of 28.1% and 29.7% respectively, outperforming two recent baselines.

By Jingtao Tang, Hang Ma
arXiv AI
Jul 15

PixelLoop: Shortcut Topological Navigation with Pixel-Level Loops

arXiv:2607. 12811v1 Announce Type: cross Abstract: Although topological mapping and navigation have been studied extensively, the specific role and downstream effect of loop closures in purely topological representations has received relatively little attention.

By Sarthak Chittawar, Vansh Garg, Aditya Vadali, Krish Pandya, Rohit Jayanti, Sourav Garg, Madhava Krishna
arXiv AI
Aug 26

Pivot-and-Station Multi-Agent Path Finding: Solvability, Complexity, and Algorithms

The paper introduces Pivot-and-Station Multi-Agent Path Finding (PS‑MAPF), a variant of MAPF where a subset of agents must visit interchangeable pivots before all agents occupy anonymous stations. It provides a full solvability characterization: every instance on a 2‑edge‑connected graph is solvable, and for arbitrary connected graphs a structural effective‑distance measure relative to unoccupied vertices gives a necessary and sufficient condition. The authors prove that minimizing station‑makespan or station‑flowtime is NP‑hard even with a single pivot, and present three algorithms—a complete baseline, a SAT‑based optimal solver, and Pivot‑Prioritized Planning (PPP), which solves 74‑89% of benchmark instances with significantly lower makespan and flowtime than the baseline.

By Andrea Di Nezza, Mihir Patel, Fabio Fagnani, Sara Bernardini