bucket-graph-spprc: an extensible C++ library for the shortest path problem with resource constraints

AlphaRoute: Large Language Models as Semantic Optimizers for Multi-Objective Routing

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. Because traditional heuristics rely on static penalty schedules that fail on complex congestion topologies, we present AlphaRoute: a multi-objective adaptive search framework reformulating rip-up and reroute (R&R) into a dynamic optimization system. We introduce SHAP-based overflow decomposition to isolate per-net congestion, driving targeted subgraph extraction via 3D Dijkstra maze routing and an adaptive PathFinder policy. Crucially, AlphaRoute employs Large Language Models (LLMs) as semantic policy optimizers. Bounded by a deterministic knowledge graph, the LLMs interpret congestion metrics to dynamically adjust penalty parameters. Evaluated on ISPD 2025 benchmarks, AlphaRoute reduces overflow by 98.6% on MEMPOOL. On the constrained ARIANE design, we achieve an overflow of 146,109 (a 29.8x reduction in overflow over the state of the art), yielding a penalized score of S_orig = 0.0538 versus the State-of-the-art (SOTA) 1.780. These results demonstrate that superior algorithmic search geometry can overcome the latency of interpreted Python implementations.

Near-Optimal Graph-Based Routing for Manual Picker-to-Parts Warehouses: A Case Study of an Apulian Distribution Center

Order picking is one of the most costly activities in manual picker-to-parts warehouses, and routing quality has a direct impact on travel effort and operational efficiency. However, commercial warehouse management systems (WMSs) still often rely on simple rule-based policies because exact optimization is difficult to reconcile with real-time execution requirements. This paper presents a WMS-compatible graph-based routing method for manual warehouses based on mission-dependent graph reduction, shortest-path computation, and sequencing optimization over mission-relevant locations. Starting from the physical warehouse graph, the proposed method builds a compact reduced representation that preserves shortest-path distances while significantly decreasing the online computational burden, enabling seamless integration into existing WMSs and real-time operation. The method is validated on a real household-goods distribution center and compared with both practical rule-based routing policies typically adopted in commercial WMSs and exact optimization benchmarks. Results on both synthetic missions and real warehouse orders show substantial travel-distance reductions with runtimes fully compatible with online warehouse operation.

DGA$_2$D: Directed Graph-Guided Automated Algorithm Design with Large Language Models

A Directed Graph-Guided Automated Algorithm Design framework, termed DGA$_2$D, which structures the open-ended program space as a directed graph, where each node represents a functional operator that can be instantiated using one of multiple candidate code implementations, while directed walks constitute complete algorithmic pipelines.

Second shortest simple paths in directed graphs: a crossing decomposition and a span-adaptive exact algorithm

Instance-Optimality of Bidirectional Dijkstra on Simple Graphs

We study the shortest-path problem on graphs with positive real-valued edge weights. Given a source vertex $s$ and a target vertex $t$, the goal is to calculate the length of the shortest path from $s$ to $t$. We are particularly interested in instances that can be solved in sublinear time. Recently, Haeupler, Hlad\'ik, Rozho\v{n}, Tarjan, and T\v{e}tek proved that (a version of) the bidirectional Dijkstra's algorithm is instance-optimal on positively weighted multigraphs, both directed and undirected, considering the number of vertices and edges queried by the algorithm. However, multigraphs are not the canonical setting for the shortest-path problem. The problem is typically formulated on simple graphs without loops and parallel edges. They therefore left as an open problem whether bidirectional Dijkstra remains instance-optimal on simple weighted graphs. We answer this question, but for simple graphs, the answer is more complex, depending on the setting. We show that bidirectional Dijkstra is still instance-optimal on simple undirected weighted graphs under the order-oblivious model, where incident edges are given in a random order. In contrast, under the order-dependent model, where incident edges have a given order, we show that bidirectional Dijkstra is not instance-optimal. For simple directed weighted graphs, we show that bidirectional Dijkstra is not instance-optimal under either the order-oblivious or the order-dependent model, being off by a factor of $\Theta(m/n)$ in both cases. We further show that no algorithm can have instance-optimality ratio $o(m/n)$ under the order-dependent model, or under the order-oblivious model when $m=O(n\sqrt{n})$. On the positive side, the above results imply that bidirectional Dijkstra is instance-optimal up to logarithmic factors on all sparse directed and undirected graphs satisfying $m/n=\log^{O(1)} n$.

A Parallel Evolutionary Algorithm Framework for Graph $k$-CUT Problems

Graph k-CUT problems include many important variants whose objectives combine cut value, volume, and cardinality terms in different ways. Most existing algorithms are designed for individual formulations, which limits their transferability across related models. In this paper, we organize a broad family of graph partitioning problems into two classes, MaxGCP and MinGCP, according to their optimization orientation and balance-related structure. Based on this classification, we propose a unified Parallel Evolutionary Algorithm Framework (PEAF). This framework combines structure-inheriting crossover operators, a hierarchical mutation mechanism based on the Multiple Mutation Heuristic (MMH) and the Auxiliary Cut Mutation Heuristic (ACMH), and a diversity-preserving selection strategy. Extensive experiments on G-set with k \in\{2, 3, 4, 5\} show that PEAF-ACMH consistently outperforms Gurobi on nine representative k-CUT problems. For MaxGCP, PEAF-ACMH improves several best-known solutions for Max-k-Cut with k \geq 3, and through numerical bounds derived from its relation to Max-k-Cut, verifies the high quality of the obtained solutions for Judicious-k-Partition and AntiCheeger-k-Cut. The results further indicate that Judicious-k-Partition usually yields more balanced partitions than AntiCheeger-k-Cut. For MinGCP, theoretical and computational comparisons show that Cheeger-k-Cut and Sparsest-k-Cut produce more balanced partitions than Normalized-k-Cut and Ratio-k-Cut, respectively. PEAF-ACMH also obtains highly similar partitions for Min-k-Cut and MinMax-k-Cut within short running times, providing numerical evidence for their structural affinity. These results demonstrate that PEAF is both an effective unified solver and a useful tool for revealing structural properties of graph k-CUT models.