Related papers: Maximum Matching sans Maximal Matching: A New Appr…
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…
We study the problem of estimating the number of triangles in a graph stream. No streaming algorithm can get sublinear space on all graphs, so methods in this area bound the space in terms of parameters of the input graph such as the…
Consider a random graph model where each possible edge $e$ is present independently with some probability $p_e$. Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we…
An $(f,g)$-semi-matching in a bipartite graph $G=(U \cup V,E)$ is a set of edges $M \subseteq E$ such that each vertex $u\in U$ is incident with at most $f(u)$ edges of $M$, and each vertex $v\in V$ is incident with at most $g(v)$ edges of…
We present a fully dynamic algorithm for maintaining approximate maximum weight matching in general weighted graphs. The algorithm maintains a matching ${\cal M}$ whose weight is at least $1/8 M^{*}$ where $M^{*}$ is the weight of the…
We consider the problem of estimating the value of max cut in a graph in the streaming model of computation. At one extreme, there is a trivial $2$-approximation for this problem that uses only $O(\log n)$ space, namely, count the number of…
We consider the classic maximal and maximum independent set problems in three models of graph streams: In the edge-arrival model we see a stream of edges which collectively define a graph, this model has been well-studied for a variety of…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
We study the problem of estimating the size of a maximum matching in sublinear time. The problem has been studied extensively in the literature and various algorithms and lower bounds are known for it. Our result is a $0.5109$-approximation…
Despite significant research efforts, the state-of-the-art algorithm for maintaining an approximate matching in fully dynamic graphs has a polynomial {worst-case} update time, even for very poor approximation guarantees. In a recent…
Many tasks in machine learning and data mining, such as data diversification, non-parametric learning, kernel machines, clustering etc., require extracting a small but representative summary from a massive dataset. Often, such problems can…
In this thesis, we explore streaming algorithms for approximating constraint satisfaction problems (CSPs). The setup is roughly the following: A computer has limited memory space, sees a long "stream" of local constraints on a set of…
Recent breakthroughs in graph streaming have led to the design of single-pass semi-streaming algorithms for various graph coloring problems such as $(\Delta+1)$-coloring, degeneracy-coloring, coloring triangle-free graphs, and others. These…
Triangle counting and sampling are two fundamental problems for streaming algorithms. Arguably, designing sampling algorithms is more challenging than their counting variants. It may be noted that triangle counting has received far greater…
In this paper, we design the first streaming algorithms for the problem of multitasking scheduling on parallel machines with shared processing. In one pass, our streaming approximation schemes can provide an approximate value of the optimal…
Given an edge-weighted metric complete graph with $n$ vertices, the maximum weight metric triangle packing problem is to find a set of $n/3$ vertex-disjoint triangles with the total weight of all triangles in the packing maximized. Several…
The stochastic matching problem deals with finding a maximum matching in a graph whose edges are unknown but can be accessed via queries. This is a special case of stochastic $k$-set packing, where the problem is to find a maximum packing…
In this paper, we study Ranking, a well-known randomized greedy matching algorithm, for general graphs. The algorithm was originally introduced by Karp, Vazirani, and Vazirani [STOC 1990] for the online bipartite matching problem with…
Recent advances in dynamic graph processing have enabled the analysis of highly dynamic graphs with change at rates as high as millions of edge changes per second. Solutions in this domain, however, have been demonstrated only for…
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to…