Related papers: A DFS Algorithm for Maximum Matchings in General G…
The problem of finding a maximum size matching in a graph (known as the maximum matching problem) is one of the most classical problems in computer science. Despite a significant body of work dedicated to the study of this problem in the…
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
Recently, great efforts have been dedicated to researches on the management of large scale graph based data such as WWW, social networks, biological networks. In the study of graph based data management, node disjoint subgraph homeomorphism…
We present a $(1- \varepsilon)$-approximation algorithms for maximum cardinality matchings in disk intersection graphs -- all with near linear running time. We also present estimation algorithm that returns $(1\pm…
Finding a maximum cardinality matching in a graph is one of the most fundamental problems. An algorithm proposed by Micali and Vazirani (1980) is well-known to solve the problem in $O(m\sqrt{n})$ time, which is still one of the fastest…
In this paper we present linear time approximation schemes for several generalized matching problems on nonbipartite graphs. Our results include $O_\epsilon(m)$-time algorithms for $(1-\epsilon)$-maximum weight $f$-factor and…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
We give a fully dynamic deterministic algorithm for maintaining a maximal matching of an $n$-vertex graph in $\tilde{O}(n^{8/9})$ amortized update time. This breaks the long-standing $\Omega(n)$-update-time barrier on dense graphs,…
Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch &…
In this paper we show how graph structure can be used to drastically reduce the computational bottleneck of the Breadth First Search algorithm (the foundation of many graph traversal techniques). In particular, we address parallel…
Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down…
Computing shortest path distances between nodes lies at the heart of many graph algorithms and applications. Traditional exact methods such as breadth-first-search (BFS) do not scale up to contemporary, rapidly evolving today's massive…
We show a fully dynamic algorithm for maintaining $(1+\epsilon)$-approximate \emph{size} of maximum matching of the graph with $n$ vertices and $m$ edges using $m^{0.5-\Omega_{\epsilon}(1)}$ update time. This is the first polynomial…
Breadth-first Search (BFS) is one of the most important graph processing subroutines, especially for computing the unweighted distance. Many applications may require running BFS from multiple sources. Sequentially, when running BFS on a…
Given a weighted digraph D, finding the longest simple path is well known to be NP-hard. Furthermore, even giving an approximation algorithm is known to be NP-hard. In this paper we describe an efficient heuristic algorithm for finding long…
The decomposition of undirected graphs simplifies complex problems by breaking them into solvable subgraphs, following the philosophy of divide and conquer. This paper investigates the relationship between atom decomposition and the maximum…
Given an undirected, anonymous, port-labeled graph of $n$ memory-less nodes, $m$ edges, and degree $\Delta$, we consider the problem of dispersing $k\leq n$ robots (or tokens) positioned initially arbitrarily on one or more nodes of the…
In this paper, we present a new exact algorithm for counting perfect matchings, which relies on neither inclusion-exclusion principle nor tree-decompositions. For any bipartite graph of $2n$ nodes and $\Delta n$ edges such that $\Delta \geq…
We study the problem of finding a maximum matching in a graph given by an input stream listing its edges in some arbitrary order, where the quantity to be maximized is given by a monotone submodular function on subsets of edges. This…