Related papers: Finding Triangles or Independent Sets; and Other D…
In the distributed triangle detection problem, we have an $n$-vertex network $G=(V,E)$ with one player for each vertex of the graph who sees the edges incident on the vertex. The players communicate in synchronous rounds using the edges of…
In this paper, we relate the problem of finding a maximum clique to the intersection number of the input graph (i.e. the minimum number of cliques needed to edge cover the graph). In particular, we consider the maximum clique problem for…
We describe a $\frac{4}{3}$-approximation algorithm for the traveling salesman problem in which the distances between points are induced by graph-theoretical distances in an unweighted graph. The algorithm is based on finding a minimum cost…
We consider the Max-$3$-Section problem, where we are given an undirected graph $ G=(V,E)$ equipped with non-negative edge weights $w :E\rightarrow \mathbb{R}_+$ and the goal is to find a partition of $V$ into three equisized parts while…
Triangle counting in hypergraph streams, including both hyper-vertex and hyper-edge triangles, is a fundamental problem in hypergraph analytics, with broad applications. However, existing methods face two key limitations: (i) an incomplete…
Recent works leveraging Graph Neural Networks to approach graph matching tasks have shown promising results. Recent progress in learning discrete distributions poses new opportunities for learning graph matching models. In this work, we…
We attempt to better understand randomization in local distributed graph algorithms by exploring how randomness is used and what we can gain from it: - We first ask the question of how much randomness is needed to obtain efficient…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
Counting the frequency of small subgraphs is a fundamental technique in network analysis across various domains, most notably in bioinformatics and social networks. The special case of triangle counting has received much attention. Getting…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of…
A clique in an undirected graph G= (V, E) is a subset V' V of vertices, each pair of which is connected by an edge in E. The clique problem is an optimization problem of finding a clique of maximum size in graph. The clique problem is…
One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel…
Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…
We present a series of almost settled inapproximability results for three fundamental problems. The first in our series is the subexponential-time inapproximability of the maximum independent set problem, a question studied in the area of…
In this paper, a polynomial time algorithm for finding the set of all cyclic subsets in a graph is presented. The concept of cyclic subsets has already been introduced in an earlier paper. The algorithm finds cyclic subsets in a graph G by…
We develop a new approach for approximating large independent sets when the input graph is a one-sided spectral expander - that is, the uniform random walk matrix of the graph has its second eigenvalue bounded away from 1. Consequently, we…
Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report…
Given a set of $n$ points $S$ in the plane, a triangulation $T$ of $S$ is a maximal set of non-crossing segments with endpoints in $S$. We present an algorithm that computes the number of triangulations on a given set of $n$ points in time…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
We study dynamic algorithms in the model of algorithms with predictions. We assume the algorithm is given imperfect predictions regarding future updates, and we ask how such predictions can be used to improve the running time. This can be…