← Back to all news
arXiv AI By Zilai Wang

An Exact 93-Move Solution to a Nonlocal Crystal-Exchange Puzzle

Read the original on arXiv AI →

The paper presents an exact 93‑move solution to a nonlocal crystal‑exchange puzzle on an 11×11 board, where a command swaps the player with the nearest crystal in a chosen row or column. The authors prove that no shorter solution exists by performing a cost‑bounded breadth‑first search that explores over 1.8 billion states, using a compressed core abstraction and several pruning conditions. The study includes a detailed description of the reductions, pruning rules, storage scheme, and provides source code, execution logs, and a reproduction driver.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

Related stories

arXiv Machine Learning
Oct 28

RadonBench: A Benchmark of Classical and Learning-Guided Search Techniques for Problems in Combinatorial Geometry

arXiv:2610. 33259v1 Announce Type: new Abstract: Classical optimization and learning-guided search offer complementary approaches to open problems in discrete mathematics, but their outputs are difficult to compare when search spaces, validity checks, and stopping rules differ.

By Xiaoan Xu, Ethan X. Fang, Jesus A. De Loera, Junwei Lu, Luze Xu
benchmarks
More like this →
arXiv AI
5d ago

A Hybrid SMT-NRA Solver: Integrating 2D Cell-Jump-Based Local Search, MCSAT and OpenCAD

The paper introduces a hybrid framework for solving Satisfiability Modulo the Theory of Nonlinear Real Arithmetic (SMT‑NRA). It presents a new two‑dimensional cell‑jump move, called 2D‑cell‑jump, that generalizes the existing cell‑jump operation by allowing search over any chosen plane. Building on this, the authors develop an extended local search framework, 2D‑LS, and combine it with MCSAT and OpenCAD to form a hybrid solver that improves search efficiency through information exchange, as shown by experimental results.

By Tianyi Ding, Haokun Li, Xinpeng Ni, Bican Xia, Tianqi Zhao
More like this →
arXiv AI
Jun 3

Finding Kissing Numbers with Game-theoretic Reinforcement Learning

arXiv:2511. 13391v4 Announce Type: replace-cross Abstract: Since Isaac Newton first studied the Kissing Number Problem in 1694, determining the maximal number of non-overlapping spheres around a central sphere has remained a defining challenge in discrete geometry.

By Chengdong Ma, Th\'eo Tao Zhaowei, Pengyu Li, Minghao Liu, Haojun Chen, Zihao Mao, Bo Li, Yuan Cheng, Yuan Qi, Yaodong Yang
reinforcement-learning
More like this →
arXiv AI
2d ago

Goal-Branching LaCAM: Temporary Goals as Search Branches in Dense Multi-Agent Pathfinding

Goal-Branching LaCAM introduces temporary goals as search branches to improve the LaCAM solver for dense multi-agent pathfinding. By assigning blocking agents temporary goals and exploring them as additional branches, the method preserves completeness while dramatically increasing success rates on dense maze and room maps. Experiments show up to 89% solved instances versus 44% for LaCAM*, with first solutions found 10–14× faster and median times nearly 200× faster at high densities, though solution cost rises modestly.

By Stephen Chang, Daniel Harabor
agentsbenchmarks
More like this →