Related papers: Towards Generating Hop-constrained s-t Simple Path…
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…
Motivated by the planarization of 2-layered straight-line drawings, we consider the problem of modifying a graph such that the resulting graph has pathwidth at most 1. The problem Pathwidth-One Vertex Explosion (POVE) asks whether such a…
A vertex in a graph dominates itself and each of its adjacent vertices. The \emph{$k$-tuple domination problem}, for a fixed positive integer $k$, is to find a minimum sized vertex subset in a given graph such that every vertex is dominated…
The girth of a graph is the length of its shortest cycle. Due to its relevance in graph theory, network analysis and practical fields such as distributed computing, girth-related problems have been object of attention in both past and…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
In the dynamic Single-Source Shortest Paths (SSSP) problem, we are given a graph $G=(V,E)$ subject to edge insertions and deletions and a source vertex $s\in V$, and the goal is to maintain the distance $d(s,t)$ for all $t\in V$.…
In this paper we revisit the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal…
Graphlets of order $k$ in a graph $G$ are connected subgraphs induced by $k$ nodes (called $k$-graphlets) or by $k$ edges (called edge $k$-graphlets). They are among the interesting subgraphs in network analysis to get insights on both the…
How efficiently can we find an unknown graph using distance or shortest path queries between its vertices? Let $G = (V,E)$ be an unweighted, connected graph of bounded degree. The edge set $E$ is initially unknown, and the graph can be…
We combine the well known Shortest Paths (SP) problem and the Bottleneck Paths (BP) problem to introduce a new problem called the Shortest Paths for All Flows (SP-AF) problem that has relevance in real life applications. We first solve the…
In the k-edge-connected spanning subgraph problem we are given a graph (V, E) and costs for each edge, and want to find a minimum-cost subset F of E such that (V, F) is k-edge-connected. We show there is a constant eps > 0 so that for all k…
Decomposing a graph into a hierarchical structure via $k$-core analysis is a standard operation in any modern graph-mining toolkit. $k$-core decomposition is a simple and efficient method that allows to analyze a graph beyond its mere…
We investigate a fundamental vertex-deletion problem called (Induced) Subgraph Hitting: given a graph $G$ and a set $\mathcal{F}$ of forbidden graphs, the goal is to compute a minimum-sized set $S$ of vertices of $G$ such that $G-S$ does…
(see paper for full abstract) Given a vertex-weighted directed graph $G=(V,E)$ and a set $T=\{t_1, t_2, \ldots t_k\}$ of $k$ terminals, the objective of the SCSS problem is to find a vertex set $H\subseteq V$ of minimum weight such that…
This paper is about the problem of finding a shortest $s$-$t$ path using at most $h$ edges in edge-weighted graphs. The Bellman--Ford algorithm solves this problem in $O(hm)$ time, where $m$ is the number of edges. We show that this running…
We show that the shortest $s$-$t$ path problem has the overlap-gap property in (i) sparse $\mathbf{G}(n,p)$ graphs and (ii) complete graphs with i.i.d. Exponential edge weights. Furthermore, we demonstrate that in sparse $\mathbf{G}(n,p)$…
A graph $G$ is $H$-saturated if it contains no copy of $H$ as a subgraph but the addition of any new edge to $G$ creates a copy of $H$. In this paper we are interested in the function sat$_{t}(n,p)$, defined to be the minimum number of…
We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut…
In the Single Source Replacement Paths (SSRP) problem we are given a graph $G = (V, E)$, and a shortest paths tree $\widehat{K}$ rooted at a node $s$, and the goal is to output for every node $t \in V$ and for every edge $e$ in…
There are many applications of graph cuts in computer vision, e.g. segmentation. We present a novel method to reformulate the NP-hard, k-way graph partitioning problem as an approximate minimal s-t graph cut problem, for which a globally…