相关论文: Minimum Label s-t Cut has Large Integrality Gaps

In this paper, we focus on the class of complete $S$-partite graphs, for $S$ an undirected graph possibly with self-loops, and address the problem of finding largest $2$-regular subgraphs of these graphs, which can be formulated as an…

Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…

In the well-known Minimum Linear Arrangement problem (MinLA), the goal is to arrange the nodes of an undirected graph into a permutation so that the total stretch of the edges is minimized. This paper studies an online (learning) variant of…

For $t,g>0$, a vertex-weighted graph of total weight $W$ is $(t,g)$-trimmable if it contains a vertex-induced subgraph of total weight at least $(1-1/t)W$ and with no simple path of more than $g$ edges. A family of graphs is trimmable if…

Assume that a graph $G$ models a detection system for a facility with a possible "intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing (the minimum number of) detectors at a…

We study two related problems: finding a set of k vertices and minimum number of edges (kmin) and finding a graph with at least m' edges and minimum number of vertices (mvms). Goldschmidt and Hochbaum \cite{GH97} show that the mvms problem…

We present a deterministic near-linear time algorithm that computes the edge-connectivity and finds a minimum cut for a simple undirected unweighted graph G with n vertices and m edges. This is the first o(mn) time deterministic algorithm…

Motivated by optimization oracles in bandits with network interference, we study the Neighborhood-Aware Graph Labeling (NAGL) problem. Given a graph $G = (V,E)$, a label set of size $L$, and local reward functions $f_v$ accessed via…

We study a general class of problems called F-deletion problems. In an F-deletion problem, we are asked whether a subset of at most $k$ vertices can be deleted from a graph $G$ such that the resulting graph does not contain as a minor any…

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…

Let $G=(V,E)$ be an undirected unweighted graph on $n$ vertices and $m$ edges. We address the problem of sensitivity oracle for all-pairs mincuts in $G$ defined as follows. Build a compact data structure that, on receiving any pair of…

We study the minimum \emph{Monitoring Edge Geodetic Set} (\megset) problem introduced in [Foucaud et al., CALDAM'23]: given a graph $G$, we say that an edge is monitored by a pair $u,v$ of vertices if \emph{all} shortest paths between $u$…

Legible labels should not overlap with other labels and other marks in a chart. When a chart contains a large number of data points, manually positioning these labels for each data point in the chart is a tedious task. A labeling algorithm…

As machine learning for images becomes democratized in the Software 2.0 era, one of the serious bottlenecks is securing enough labeled data for training. This problem is especially critical in a manufacturing setting where smart factories…

We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less…

This paper introduces the \emph{$d$-distance matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges and an integer $d\in\mathbb Z_+$. The goal is to find a maximum…

Optimization problems consist of either maximizing or minimizing an objective function. Instead of looking for a maximum solution (resp. minimum solution), one can find a minimum maximal solution (resp. maximum minimal solution). Such…

We develop new $(1+\epsilon)$-approximation algorithms for finding the global minimum edge-cut in a directed edge-weighted graph, and for finding the global minimum vertex-cut in a directed vertex-weighted graph. Our algorithms are…

We study the minimum cut problem in the presence of uncertainty and show how to apply a novel robust optimization approach, which aims to exploit the similarity in subsequent graph measurements or similar graph instances, without posing any…

Subgraph Isomorphism is a very basic graph problem, where given two graphs $G$ and $H$ one is to check whether $G$ is a subgraph of $H$. Despite its simple definition, the Subgraph Isomorphism problem turns out to be very broad, as it…