相关论文: Exact Shortest Paths with Rational Weights on the …

We present new deterministic algorithms for computing distributed weighted minimum weight cycle (MWC) in undirected and directed graphs and distributed weighted all nodes shortest cycle (ANSC) in directed graphs. Our algorithms for these…

We give a quantum algorithm to exactly solve certain problems in combinatorial optimization, including weighted MAX-2-SAT as well as problems where the objective function is a weighted sum of products of Ising variables, all terms of the…

We consider the problem of finding ``dissimilar'' $k$ shortest paths from $s$ to $t$ in an edge-weighted directed graph $D$, where the dissimilarity is measured by the minimum pairwise Hamming distances between these paths. More formally,…

We describe algorithms to efficiently compute minimum $(s,t)$-cuts and global minimum cuts of undirected surface-embedded graphs. Given an edge-weighted undirected graph $G$ with $n$ vertices embedded on an orientable surface of genus $g$,…

We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. The allowed updates are insertions and deletions of nodes and their incident edges. We give worst-case…

Let $G$ be a unit disk graph in the plane defined by $n$ disks whose positions are known. For the case when $G$ is unweighted, we give a simple algorithm to compute a shortest path tree from a given source in $O(n\log n)$ time. For the case…

Consider a random regular graph with degree $d$ and of size $n$. Assign to each edge an i.i.d. exponential random variable with mean one. In this paper we establish a precise asymptotic expression for the maximum number of edges on the…

The shortest paths problem is a fundamental challenge in graph theory, with a broad range of potential applications. The algorithms based on matrix multiplication exhibits excellent parallelism and scalability, but is constrained by high…

We obtain the first near-linear time deterministic algorithm for negative-weight single-source shortest paths on integer-weighted graphs. Our main ingredient is a deterministic construction of a padded decomposition on directed graphs,…

We propose an optimal algorithm for solving the longest path problem in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art…

Given a set P of n points in the plane, the unit-disk graph G_{r}(P) with respect to a parameter r is an undirected graph whose vertex set is P such that an edge connects two points p, q \in P if the Euclidean distance between p and q is at…

As the popularity of graph data increases, there is a growing need to count the occurrences of subgraph patterns of interest, for a variety of applications. Many graphs are massive in scale and also fully dynamic (with insertions and…

We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…

We study the fully dynamic All-Pairs Shortest Paths (APSP) problem in undirected edge-weighted graphs. Given an $n$-vertex graph $G$ with non-negative edge lengths, that undergoes an online sequence of edge insertions and deletions, the…

Let $S$ be a set of $n$ points in a polygon $P$ with $m$ vertices. The geodesic unit-disk graph $G(S)$ induced by $S$ has vertex set $S$ and contains an edge between two vertices whenever their geodesic distance in $P$ is at most one. In…

Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: If the edges are given…

We study the problem of computing the minimum cut in a weighted distributed message-passing networks (the CONGEST model). Let $\lambda$ be the minimum cut, $n$ be the number of nodes in the network, and $D$ be the network diameter. Our…

We present a universally-optimal distributed algorithm for the exact weighted min-cut. The algorithm is guaranteed to complete in $\widetilde{O}(D + \sqrt{n})$ rounds on every graph, recovering the recent result of Dory, Efron,…

Given an arbitrary, non-negatively weighted, directed graph $G=(V,E)$ we present an algorithm that computes all pairs shortest paths in time $\mathcal{O}(m^* n + m \lg n + nT_\psi(m^*, n))$, where $m^*$ is the number of different edges…

This paper shows the weighted matching problem on general graphs can be solved in time $O(n(m + n\log n))$ for $n$ and $m$ the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a…