Related papers: Improving The Floyd-Warshall All Pairs Shortest Pa…
In the $k$-Disjoint Shortest Paths ($k$-DSP) problem, we are given a weighted graph $G$ on $n$ nodes and $m$ edges with specified source vertices $s_1, \dots, s_k$, and target vertices $t_1, \dots, t_k$, and are tasked with determining if…
Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow/circulation $X$ on a directed graph $G$ into weighted source-to-sink paths whose superposition equals $X$. We show that, for…
Identifying shortest paths between nodes in a network is an important task in many applications. Recent work has shown that a malicious actor can manipulate a graph to make traffic between two nodes of interest follow their target path. In…
In this paper we prove that Dijkstra's shortest-path algorithm, if implemented with a sufficiently efficient heap, is universally optimal in its running time, and with suitable small additions is also universally optimal in its number of…
We initiate the study of approximation algorithms and computational barriers for constructing sparse $\alpha$-navigable graphs [IX23, DGM+24], a core primitive underlying recent advances in graph-based nearest neighbor search. Given an…
Using Dijkstra's algorithm to compute the shortest paths in a graph from a single source node to all other nodes is common practice in industry and academia. Although the original description of the algorithm advises using a Fibonacci Heap…
We perform an experimental evaluation of algorithms for finding geodesic shortest paths between two points inside a simple polygon in the constant-workspace model. In this model, the input resides in a read-only array that can be accessed…
The widespread use of graph data in various applications and the highly dynamic nature of today's networks have made it imperative to analyze structural trends in dynamic graphs on a continual basis. The shortest path is a fundamental…
We consider the problem of computing shortest paths in weighted unit-disk graphs in constant dimension $d$. Although the single-source and all-pairs variants of this problem are well-studied in the plane case, no non-trivial exact distance…
In this paper, we propose a depth-first search (DFS) algorithm for searching maximum matchings in general graphs. Unlike blossom shrinking algorithms, which store all possible alternative alternating paths in the super-vertices shrunk from…
Study the general single-source shortest path problem. Firstly, define a path function on a set of some path with same source on a graph, and develop a kind of general single-source shortest path problem (GSSSP) on the defined path…
A hypergraph is a set V of vertices and a set of non-empty subsets of V, called hyperedges. Unlike graphs, hypergraphs can capture higher-order interactions in social and communication networks that go beyond a simple union of pairwise…
Shortest paths in complex networks play key roles in many applications. Examples include routing packets in a computer network, routing traffic on a transportation network, and inferring semantic distances between concepts on the World Wide…
Computing shortest path distances between nodes lies at the heart of many graph algorithms and applications. Traditional exact methods such as breadth-first-search (BFS) do not scale up to contemporary, rapidly evolving today's massive…
In this paper we show a deterministic parallel all-pairs shortest paths algorithm for real-weighted directed graphs. The algorithm has $\tilde{O}(nm+(n/d)^3)$ work and $\tilde{O}(d)$ depth for any depth parameter $d\in [1,n]$. To the best…
In this paper, I present an algorithm called Raffica algorithm for Single-Source Shortest Path(SSSP). On random graph, this algorithm has linear time complexity(in expect). More precisely, the random graph uses configuration model, and the…
In this paper, we present a polynomial time algorithm for the problem of differentially private all pair shortest distances over the class of low tree-width graphs. Our result generalizes the result of Sealfon 2016 for the case of trees to…
The composition problem for shortest paths asks the following: given shortest paths on weighted graphs M and N which share a common boundary, find the shortest paths on their union. This problem is a crucial step in any algorithm which uses…
Given a weighted digraph D, finding the longest simple path is well known to be NP-hard. Furthermore, even giving an approximation algorithm is known to be NP-hard. In this paper we describe an efficient heuristic algorithm for finding long…
The replacement paths problem for directed graphs is to find for given nodes s and t and every edge e on the shortest path between them, the shortest path between s and t which avoids e. For unweighted directed graphs on n vertices, the…