Related papers: Finding a Shortest Non-zero Path in Group-Labeled …
We give the first polynomial-time algorithms on graphs of bounded maximum induced matching width (mim-width) for problems that are not locally checkable. In particular, we give $n^{\mathcal{O}(w)}$-time algorithms on graphs of mim-width at…
The shortest secure path (routing) problem in communication networks has to deal with multiple attack layers e.g., man-in-the-middle, eavesdropping, packet injection, packet insertion, etc. Consider different probabilities for each such…
We initiate the study of the shortest reconfiguration problem for independent sets under the adjacency relation derived from the independent set polytope. Given a graph and two independent sets, the problem asks for a shortest sequence…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
In this paper, we give a new framework for the stochastic shortest path problem in finite state and action spaces. Our framework generalizes both the frameworks proposed by Bertsekas and Tsitsikli and by Bertsekas and Yu. We prove that the…
We propose a consistent polynomial-time method for the unseeded node matching problem for networks with smooth underlying structures. Despite widely conjectured by the research community that the structured graph matching problem to be…
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…
We give the first parallel algorithm with optimal $\tilde{O}(m)$ work for the classical problem of computing Single-Source Shortest Paths in general graphs with negative-weight edges. In graphs without negative edges, Dijkstra's algorithm…
In this paper, we revisit the classic approximate All-Pairs Shortest Paths (APSP) problem in undirected graphs. For unweighted graphs, we provide an algorithm for $2$-approximate APSP in $\tilde O(n^{2.5-r}+n^{\omega(r)})$ time, for any…
The $k$ disjoint shortest paths problem ($k$-DSPP) on a graph with $k$ source-sink pairs $(s_i, t_i)$ asks for the existence of $k$ pairwise edge- or vertex-disjoint shortest $s_i$-$t_i$-paths. It is known to be NP-complete if $k$ is part…
In Polyamorous Scheduling, we are given an edge-weighted graph and must find a periodic schedule of matchings in this graph which minimizes the maximal weighted waiting time between consecutive occurrences of the same edge. This NP-hard…
In the Disjoint Paths problem, the input consists of an $n$-vertex graph $G$ and a collection of $k$ vertex pairs, $\{(s_i,t_i)\}_{i=1}^k$, and the objective is to determine whether there exists a collection $\{P_i\}_{i=1}^k$ of $k$…
In this paper, we study a set of combinatorial optimization problems on weighted graphs: the shortest path problem with negative weights, the weighted perfect bipartite matching problem, the unit-capacity minimum-cost maximum flow problem…
The exact matching problem is a constrained variant of the maximum matching problem: given a graph with each edge having a weight $0$ or $1$ and an integer $k$, the goal is to find a perfect matching of weight exactly $k$. Mulmuley,…
This paper discusses the shortest path problem in a general directed graph with $n$ nodes and $K$ cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to…
Given a directed graph $G$ with arbitrary real-valued weights, the single source shortest-path problem (SSSP) asks for, given a source $s$ in $G$, finding a shortest path from $s$ to each vertex $v$ in $G$. A classical SSSP algorithm…
In this work we study shortest path problems in multimode graphs, a generalization of the min-distance measure introduced by Abboud, Vassilevska W. and Wang in [SODA'16]. A multimode shortest path is the shortest path using one of multiple…
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…
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…
In this paper, we show that given a weighted, directed planar graph $G$, and any $\epsilon >0$, there exists a polynomial time and $O(n^{\frac{1}{2}+\epsilon})$ space algorithm that computes the shortest path between two fixed vertices in…