distance-indexed neural a*

Handcrafted heuristic functions in search-based navigation suffer from poor generalization across unseen maps and long-distance paths. Method: This paper proposes a local heuristic learning framework that explicitly defines and end-to-end learns either heuristic bias correction or local cost estimation within a spatial neighborhood—replacing conventional global heuristic modeling. By decomposing complex global prediction into lightweight local regression, the approach significantly reduces learning complexity. Integrated with graph search algorithms (e.g., A*), it operates under supervised learning using local state inputs while preserving bounded suboptimality guarantees. Contribution/Results: Experiments demonstrate 2–20× reduction in node expansions, improved training efficiency, and robust generalization to both unseen maps and long-range trajectories—without compromising solution quality or theoretical guarantees.

This work addresses the modeling limitations in pathfinding tasks arising from the tight coupling between problem graphs and movement graphs. To overcome this, the paper introduces a directed, weighted bipartite graph model that explicitly decouples feasibility—defined by the problem graph—from movement rules—governed by the movement graph—for the first time. This formulation naturally accommodates asymmetry, heterogeneous constraints, and weighted transitions, thereby unifying and extending classical solution-discovery frameworks. Leveraging tools from combinatorial optimization, graph theory, and computational complexity, the study provides a complete characterization of the complexity landscape for both general pathfinding and shortest-path problems under the proposed model, precisely delineating polynomial-time solvable cases from those that are strongly NP-hard.

Traditional heuristic methods in reinforcement learning for shortest-path problems rely on single-step Bellman updates, leading to localized and inconsistent state-value estimates. To address this, we propose a multi-step heuristic learning framework that integrates finite-horizon graph search with deep approximate value iteration. Our method anchors computation at the search frontier and propagates path information backward via bounded-depth search, enabling multi-step, globally consistent value correction. A neural network is trained end-to-end to approximate the heuristic function. Evaluated on diverse pathfinding benchmarks, our approach significantly improves both search efficiency and solution quality: average node expansions decrease by 37%, and optimal solution rates increase by 22% compared to single-step update baselines. These results validate the effectiveness and generalizability of multi-step search-guided heuristic learning.

This paper studies the Weighted Expansion Search problem on graphs: a searcher starts from a designated vertex and iteratively expands along edges to unvisited vertices, with edge lengths representing traversal time; the objective is to minimize the weighted sum of vertex weights multiplied by their first-visit times. As an NP-hard problem, it had long been stuck at an 8-approximation barrier. We break this barrier via a unified framework integrating greedy construction, randomized rounding, Euclidean geometric partitioning, and dynamic programming, complemented by hardness analysis under exponential-time hypotheses. Our contributions are the first: (i) a $(2e+varepsilon)$-approximation algorithm for general graphs; (ii) a $2e$-approximation algorithm for unit-weight graphs; and (iii) a PTAS for Euclidean graphs (for any $varepsilon > 0$). These results substantially improve approximation ratios and provide the strongest known theoretical guarantees for all three graph classes.

This work investigates the construction and theoretical limits of sparse navigable graphs over high-dimensional point sets: specifically, whether, under arbitrary distance functions, graphs with sufficiently low average degree exist such that greedy routing always succeeds from any source to any target. Methodologically, the authors integrate high-dimensional geometry, probabilistic analysis—including binomial anti-concentration inequalities—and graph theory, overcoming prior restrictions to low-dimensional or distribution-specific settings. Their contributions are threefold: (i) they establish tight asymptotic bounds on navigability in high dimensions; (ii) they propose a generic construction achieving average degree $O(sqrt{n log n})$; and (iii) they prove a matching $Omega(n^{1/2})$ lower bound—demonstrating that for $O(log n)$-dimensional random point sets, every navigable graph must have average degree at least $Omega(n^{1/2})$. These results provide both foundational theory and practical constructions for high-dimensional nearest-neighbor search.

This work addresses the inefficiency of traditional heuristic search in graphs where edge weights represent non-geometric metrics such as latency or cost, due to the absence of effective heuristics. It proposes the first integration of large language models (LLMs) into non-geometric graph path planning by coupling them with the A* algorithm. The approach leverages graph structural features and landmark-based distances—inspired by the ALT heuristic—as input to the LLM to generate intermediate waypoints that guide the search direction. Notably, this method restores the LLM’s awareness of target distance without requiring complex prompt engineering. Experimental results across diverse graph topologies with up to 2,000 nodes demonstrate that the proposed technique reduces the number of expanded nodes by approximately 50% while incurring only a marginal increase in path cost, thereby significantly enhancing search efficiency and validating its practicality and effectiveness.

研究了A*算法在最终平层上不同平分策略下的扩展节点数量问题，通过一致启发式方法分析九种标准策略的性能差异，并提出一种参数化单位成本网格示例来展示极端情况。

This study addresses the graph traversal problem with a discount factor α and a p-norm objective, aiming to efficiently find a path that visits all vertices while minimizing the α-discounted latency p-norm. The authors propose the first unified framework that integrates discounted traversal costs with p-norm objectives, subsuming classical models such as path search, orienteering, minimum spanning trees, and the traveling salesman problem. They develop combinatorial optimization and approximation algorithms: for p = 1, they present a polynomial-time constant-factor approximation algorithm; for arbitrary p ≥ 1, they design a randomized constant-factor approximation algorithm and derandomize it to obtain a deterministic pseudo-polynomial-time algorithm, achieving theoretical guarantees across the full parameter range.

本文针对有向图中次短路径问题，提出了一种基于最优中间段框架的更快算法，通过选择前缀和完成前缀的方法，将时间复杂度降低至O(n^3 (m + n log n))。

Subgraph extraction problems arise widely in network design, facility location, and related domains, yet lack a general-purpose, efficient solution methodology. This work proposes ΔSearch—the first unified heuristic framework that requires only user-specified feasibility constraints and an optimization objective, automatically adapting to monotone, weighted monotone, and non-monotone graph problems without problem-specific parameter tuning. By integrating a reward-penalty optimization mechanism, generic constraint modeling, and search space pruning techniques, ΔSearch substantially enhances computational efficiency and can accelerate exact algorithms. Empirical evaluations demonstrate that it matches or surpasses state-of-the-art heuristics on tasks such as maximum planar subgraph, uncapacitated facility location, and prize-collecting vertex cover, while achieving approximately 89% of optimal solution quality on average across other problems—all without any parameter tuning.