arXiv:2606. 05956v1 Announce Type: new Abstract: Bidirectional heuristic search can potentially reduce search effort for problems amenable to backward search.
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arXiv:2606. 07047v1 Announce Type: new Abstract: Heuristics play a central role in the performance of bidirectional search algorithms, which commonly rely on two main classes.
Probabilistic Focal Search (PFS) augments traditional Focal Search by probabilistically choosing between the standard heuristic-guided expansion and expanding the minimum‑f node in OPEN. This strategy advances the lower bound, enlarges the FOCAL frontier, and can dramatically reduce node expansions—up to 90% in some benchmarks such as N‑Puzzle and TSP—especially when long f_min plateaus delay useful FOCAL admissions. An anytime variant, APFS, outperforms other tested anytime algorithms on the Generalized Covering TSP, and the same probabilistic scheduler transfers to Dynamic Potential Search as Probabilistic Dynamic Potential Search (PDPS), though its effectiveness varies by domain and bound.
arXiv:2607. 19768v1 Announce Type: new Abstract: Very Large Scale Integration (VLSI) global routing is an NP-hard combinatorial optimization problem requiring signal net assignment across capacity-constrained 3D grids while minimizing congestion, wirelength, and via transitions.
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.
arXiv:2606. 06618v1 Announce Type: cross Abstract: How can we plan long-horizon routes that reach designated goals, visit required waypoints, and remain short when only short-horizon offline trajectories are available?
arXiv:2609.23293v1 Announce Type: new Abstract: In the A* search algorithm, the tie-breaking strategies for nodes with the same $f$-value determines which states A* expands on the final $f$-layer. Fo...