Related papers: Finding a Shortest Non-zero Path in Group-Labeled …
The isomorphism problem for graphs (GI) and the isomorphism problem for groups (GrISO) have been studied extensively by researchers. The current best algorithms for both these problems run in quasipolynomial time. In this paper, we study…
Given a set of well-formed terminal pairs on the external face of an undirected planar graph with unit edge weights, we give a linear-time algorithm for computing the union of non-crossing shortest paths joining each terminal pair, where…
This paper presents near-optimal deterministic parallel and distributed algorithms for computing $(1+\varepsilon)$-approximate single-source shortest paths in any undirected weighted graph. On a high level, we deterministically reduce this…
We consider the directed minimum weight cycle problem in the fully dynamic setting. To the best of our knowledge, so far no fully dynamic algorithms have been designed specifically for the minimum weight cycle problem in general digraphs.…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
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…
We present polylogarithmic approximation algorithms for variants of the Shortest Path, Group Steiner Tree, and Group ATSP problems with vector costs. In these problems, each edge e has a non-negative vector cost $c_e \in…
Python implementation of selected weighted graph algorithms is presented. The minimal graph interface is defined together with several classes implementing this interface. Graph nodes can be any hashable Python objects. Directed edges are…
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…
Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm…
We show that for each fixed $k$, the problem of finding $k$ pairwise vertex-disjoint directed paths between given source-sink pairs in a planar directed graph is solvable in polynomial time. In fact, it suffices to fix the number of faces…
We present a very simple and intuitive algorithm to find balanced sparse cuts in a graph via shortest-paths. Our algorithm combines a new multiplicative-weights framework for solving unit-weight multi-commodity flows with standard ball…
Solving the shortest path and the min-cut problems are key in achieving high performance and robust communication networks. Those problems have often beeny studied in deterministic and independent networks both in their original…
We present a deterministic $(1+o(1))$-approximation $(n^{1/2+o(1)}+D^{1+o(1)})$-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the CONGEST model); here $n$ is the number of nodes in the…
Given a simple weighted directed graph $G = (V, E, \omega)$ on $n$ vertices as well as two designated terminals $s, t\in V$, our goal is to compute the shortest path from $s$ to $t$ avoiding any pair of presumably failed edges $f_1, f_2\in…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
We present the first non-trivial fully dynamic algorithm maintaining exact single-source distances in unweighted graphs. This resolves an open problem stated by Sankowski [COCOON 2005] and van den Brand and Nanongkai [FOCS 2019]. Previous…
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…
The paper deals with finite-state Markov decision processes (MDPs) with integer weights assigned to each state-action pair. New algorithms are presented to classify end components according to their limiting behavior with respect to the…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…