Related papers: Near-Optimal Four-Cycle Counting in Graph Streams
Space complexity is a critical factor in various computational models, including streaming, parallel/distributed computing, and communication complexity. We study the space complexity of the minimum-cost flow problem, a generalization of…
We present an $\tilde O(m+n^{1.5})$-time randomized algorithm for maximum cardinality bipartite matching and related problems (e.g. transshipment, negative-weight shortest paths, and optimal transport) on $m$-edge, $n$-node graphs. For…
We extend the multi-pass streaming model to sliding window problems, and address the problem of computing order statistics on fixed-size sliding windows, in the multi-pass streaming model as well as the closely related communication…
This paper presents a quantum algorithm for triangle finding over sparse graphs that improves over the previous best quantum algorithm for this task by Buhrman et al. [SIAM Journal on Computing, 2005]. Our algorithm is based on the recent…
We obtain some new upper bounds on the maximum number $f(n)$ of edges in $n$-vertex graphs without containing cycles of length four. This leads to an asymptotically optimal bound on $f(n)$ for a broad range of integers $n$ as well as a…
Vizing's celebrated theorem states that every simple graph with maximum degree $\Delta$ admits a $(\Delta+1)$ edge coloring which can be found in $O(m \cdot n)$ time on $n$-vertex $m$-edge graphs. This is just one color more than the…
The Path Contraction and Cycle Contraction problems take as input an undirected graph $G$ with $n$ vertices, $m$ edges and an integer $k$ and determine whether one can obtain a path or a cycle, respectively, by performing at most $k$ edge…
We present a deterministic $n^{2+o(1)}$-time algorithm that approximates the crossing number of any graph $G$ of order $n$ up to an additive error of $o(n^4)$. We also provide a randomized polynomial-time algorithm that constructs a drawing…
We present the first truly subcubic, combinatorial algorithm for detecting an induced $4$-cycle in a graph. The running time is $O(n^{2.84})$ on $n$-node graphs, thus separating the task of detecting induced $4$-cycles from detecting…
The Fr\'echet distance is a popular distance measure between trajectories or curves in space, or between walks in graphs. We study computing the Fr\'echet distance between walks in the $d$-dimensional grid graphs, i.e. $\mathbb{Z}^d$ where…
We describe a general purpose algorithm for counting simple cycles and simple paths of any length $\ell$ on a (weighted di)graph on $N$ vertices and $M$ edges, achieving a time complexity of $O\left(N+M+\big(\ell^\omega+\ell\Delta\big)…
Given a graph stream, how can we estimate the number of triangles in it using multiple machines with limited storage? Specifically, how should edges be processed and sampled across the machines for rapid and accurate estimation? The count…
We present a simple nonadaptive randomized algorithm that estimates the number of edges in a simple, unweighted, undirected graph, possibly containing isolated vertices, using only degree and random edge queries. For an $n$-vertex graph,…
The Steiner Multicycle problem consists of, given a complete graph, a weight function on its vertices, and a collection of pairwise disjoint non-unitary sets called terminal sets, finding a minimum weight collection of vertex-disjoint…
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…
We prove $n^{1+\Omega(1/p)}/p^{O(1)}$ lower bounds for the space complexity of $p$-pass streaming algorithms solving the following problems on $n$-vertex graphs: * testing if an undirected graph has a perfect matching (this implies lower…
In this paper, we consider three hitting problems on a disk intersection graph: Triangle Hitting Set, Feedback Vertex Set, and Odd Cycle Transversal. Given a disk intersection graph $G$, our goal is to compute a set of vertices hitting all…
We give an $\widetilde{O}(\sqrt{n})$-space single-pass $0.483$-approximation streaming algorithm for estimating the maximum directed cut size (Max-DICUT) in a directed graph on $n$ vertices. This improves over an $O(\log n)$-space $4/9 <…
We give improved multi-pass streaming algorithms for the problem of maximizing a monotone or arbitrary non-negative submodular function subject to a general $p$-matchoid constraint in the model in which elements of the ground set arrive one…
We present an algorithm for computing $s$-$t$ maximum flows in directed graphs in $\widetilde{O}(m^{4/3+o(1)}U^{1/3})$ time. Our algorithm is inspired by potential reduction interior point methods for linear programming. Instead of using…