Related papers: A Proof of the MV Matching Algorithm
In this paper we present improved bounds for approximating maximum matchings in bipartite graphs in the streaming model. First, we consider the question of how well maximum matching can be approximated in a single pass over the input using…
We present an algorithm that enumerates all the perfect matchings in a given bipartite graph G = (V,E). Our algorithm requires a constant amortized time to visit one perfect matching of G, in contrast to the current fastest algorithm,…
In the Minimum Consistent Subset (MCS) problem, we are presented with a connected simple undirected graph $G=(V,E)$, consisting of a vertex set $V$ of size $n$ and an edge set $E$. Each vertex in $V$ is assigned a color from the set…
Randomized greedy algorithms form one of the simplest yet most effective approaches for computing approximate matchings in graphs. In this paper, we focus on the class of vertex-iterative (VI) randomized greedy matching algorithms, which…
A bipartite graph $G(U,V;E)$ that admits a perfect matching is given. One player imposes a permutation $\pi$ over $V$, the other player imposes a permutation $\sigma$ over $U$. In the greedy matching algorithm, vertices of $U$ arrive in…
Given a graph in which a few vertices are deemed interesting a priori, the vertex nomination task is to order the remaining vertices into a nomination list such that there is a concentration of interesting vertices at the top of the list.…
The bipartite matching problem in the online and streaming settings has received a lot of attention recently. The classical vertex arrival setting, for which the celebrated Karp, Vazirani and Vazirani (KVV) algorithm achieves a $1-1/e$…
The maximum clique problem (MCP) is a fundamental problem in graph theory and in computational complexity. Given a graph G, the problem is that of finding the largest clique (complete subgraph) in G. The MCP has many important applications…
The modularity is a quality function in community detection, which was introduced by Newman and Girvan (2004). Community detection in graphs is now often conducted through modularity maximization: given an undirected graph $G=(V,E)$, we are…
A temporal graph is a sequence of graphs (called layers) over the same vertex set -- describing a graph topology which is subject to discrete changes over time. A $\Delta$-temporal matching $M$ is a set of time edges $(e,t)$ (an edge $e$…
The Maximum Carpool Matching problem is a star packing problem in directed graphs. Formally, given a directed graph $G = (V, A)$, a capacity function $ c: V \to N $, and a weight function $w : A \to R $, a feasible \emph{carpool matching}…
Alspach [ Bull. Inst. Combin. Appl., 52 (2008), pp. 7-20] defined the maximal matching sequencibility of a graph $G$, denoted $ms(G)$, to be the largest integer $s$ for which there is an ordering of the edges of $G$ such that every $s$…
In this paper, we study the maximum matching problem in RDV graphs, i.e., graphs that are vertex-intersection graphs of downward paths in a rooted tree. We show that this problem can be reduced to a problem of testing (repeatedly) whether a…
Is matching in NC, i.e., is there a deterministic fast parallel algorithm for it? This has been an outstanding open question in TCS for over three decades, ever since the discovery of randomized NC matching algorithms [KUW85, MVV87]. Over…
We consider the problem of finding a maximum size triangle-free $2$-matching in a graph $G=(V,E)$. A (simple) $2$-matching is any subset of the edges such that each vertex is incident to at most two edges from the subset. The first…
We present a massively parallel algorithm, with near-linear memory per machine, that computes a $(2+\varepsilon)$-approximation of minimum-weight vertex cover in $O(\log\log d)$ rounds, where $d$ is the average degree of the input graph.…
A Meyniel graph is a graph in which every odd cycle of length at least five has two chords. In the manuscript "Coloring Meyniel graphs in linear time" we claimed that our algorithm MCColor produces an optimal coloring for every Meyniel…
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…
A recent breakthrough of Behnezhad and Ghafari [FOCS 2024] and subsequent work of Assadi, Khanna, and Kiss [SODA 2025] gave algorithms for the fully dynamic $(1-\varepsilon)$-approximate maximum matching problem whose runtimes are…
Let G=(V,E) be a graph with f:V\to Z_+ a function assigning degree bounds to vertices. We present the first efficient algebraic algorithm to find an f-factor. The time is \tilde{O}(f(V)^{\omega}). More generally for graphs with integral…