Related papers: Some Extensions of the All Pairs Bottleneck Paths …
We consider the Shortest Odd Path problem, where given an undirected graph $G$, a weight function on its edges, and two vertices $s$ and $t$ in $G$, the aim is to find an $(s,t)$-path with odd length and, among all such paths, of minimum…
In this paper, we investigate offline and online algorithms for rufpp, the problem of minimizing the number of rounds required to schedule a set of unsplittable flows of non-uniform sizes on a given path with non-uniform edge capacities.…
Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…
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 the k-Disjoint Shortest Paths problem, a set of terminal pairs of vertices $\{(s_i,t_i)\mid 1\le i\le k\}$ is given and we are asked to find paths $P_1,\ldots,P_k$ such that each path $P_i$ is a shortest path from $s_i$ to $t_i$ and…
We investigate the problem of computing the top-$k$ simple shortest paths in weighted digraphs. While the single-pair variant -- finding the top-$k$ simple shortest paths between two specified vertices -- has been extensively studied over…
We consider the problem of locating a set of $k$ sinks on a path network with general edge capacities that minimizes the sum of the evacuation times of all evacuees. We first present an $O(kn\log^4n)$ time algorithm when the edge capacities…
In the decremental $(1+\epsilon)$-approximate Single-Source Shortest Path (SSSP) problem, we are given a graph $G=(V,E)$ with $n = |V|, m = |E|$, undergoing edge deletions, and a distinguished source $s \in V$, and we are asked to process…
The approximate single-source shortest-path problem is as follows: given a graph with nonnegative edge weights and a designated source vertex $s$, return estimates of the distances from~$s$ to each other vertex such that the estimate falls…
We present a combinatorial algorithm for computing exact maximum flows in directed graphs with $n$ vertices and edge capacities from $\{1,\dots,U\}$ in $n^{2+o(1)}\log U$ time, which is almost optimal in dense graphs. Our algorithm is a…
In a series of papers, Avraham, Filtser, Kaplan, Katz, and Sharir (SoCG'14), Kaplan, Katz, Saban, and Sharir (ESA'23), and Katz, Saban, and Sharir (ESA'24) studied a class of geometric optimization problems -- including reverse shortest…
We consider the fine-grained complexity of sparse graph problems that currently have $\tilde{O}(mn)$ time algorithms, where m is the number of edges and n is the number of vertices in the input graph. This class includes several important…
We investigate the single-source-single-destination "shortest" paths problem in acyclic graphs with ordinal weighted arc costs. We define the concepts of ordinal dominance and efficiency for paths and their associated ordinal levels,…
We consider the quantum time complexity of the all pairs shortest paths (APSP) problem and some of its variants. The trivial classical algorithm for APSP and most all pairs path problems runs in $O(n^3)$ time, while the trivial algorithm in…
Let $G$ be an edge-weighted directed graph with $n$ vertices embedded on an orientable surface of genus $g$. We describe a simple deterministic lexicographic perturbation scheme that guarantees uniqueness of minimum-cost flows and shortest…
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 textbook algorithm for real-weighted single-source shortest paths takes $O(m n)$ time on a graph with $m$ edges and $n$ vertices. The breakthrough algorithm by Fineman [Fin24] takes $\tilde{O}(m n^{8/9})$ randomized time. The running…
We introduce a new bilevel version of the classic shortest path problem and completely characterize its computational complexity with respect to several problem variants. In our problem, the leader and the follower each control a subset of…
Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…
We consider a constrained version of the shortest path problem on the complete graphs whose edges have independent random lengths and costs. We establish the asymptotic value of the minimum length as a function of the cost-budget within a…