Related papers: Markovian online matching algorithms on large bipa…
We study the on-line minimum weighted bipartite matching problem in arbitrary metric spaces. Here, $n$ not necessary disjoint points of a metric space $M$ are given, and are to be matched on-line with $n$ points of $M$ revealed one by one.…
We present a polylogarithmic local computation matching algorithm which guarantees a $(1-\eps)$-approximation to the maximum matching in graphs of bounded degree.
Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…
We consider the algorithmic problem of finding large \textit{balanced} independent sets in sparse random bipartite graphs, and more generally the problem of finding independent sets with specified proportions of vertices on each side of the…
Matching, a task to optimally assign limited resources under constraints, is a fundamental technology for society. The task potentially has various objectives, conditions, and constraints; however, the efficient neural network architecture…
We study generalizations of online bipartite matching in which each arriving vertex (customer) views a ranked list of offline vertices (products) and matches to (purchases) the first one they deem acceptable. The number of products that the…
Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and…
We consider the online bipartite matching problem on $(k,d)$-bounded graphs, where each online vertex has at most $d$ neighbors, each offline vertex has at least $k$ neighbors, and $k\geq d\geq 2$. The model of $(k,d)$-bounded graphs is…
We resolve the fundamental problem of online decoding with general $n^{th}$ order ergodic Markov chain models. Specifically, we provide deterministic and randomized algorithms whose performance is close to that of the optimal offline…
Motivated by display advertising on the internet, the online stochastic matching problem is proposed by Feldman, Mehta, Mirrokni, and Muthukrishnan (FOCS 2009). Consider a stochastic bipartite graph with offline vertices on one side and…
In this paper, we study the problem of recovering the latent vertex correspondence between two correlated random graphs with vastly inhomogeneous and unknown edge probabilities between different pairs of vertices. Inspired by and extending…
A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph…
In this paper we analyze the expected time complexity of the auction algorithm for the matching problem on random bipartite graphs. We prove that the expected time complexity of the auction algorithm for bipartite matching is…
We study approximations of the partition function of dense graphical models. Partition functions of graphical models play a fundamental role is statistical physics, in statistics and in machine learning. Two of the main methods for…
An important objective for analyzing real-world graphs is to achieve scalable performance on large, streaming graphs. A challenging and relevant example is the graph partition problem. As a combinatorial problem, graph partition is NP-hard,…
We study numerically the maximum $z$-matching problems on ensembles of bipartite random graphs. The $z$-matching problems describes the matching between two types of nodes, users and servers, where each server may serve up to $z$ users at…
We consider the problem of sequential matching in a stochastic block model with several classes of nodes and generic compatibility constraints. When the probabilities of connections do not scale with the size of the graph, we show that…
Graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most graph clustering algorithms is to find a vertex set of low…
Local complement is a graph operation formalized by Bouchet which replaces the neighborhood of a chosen vertex with its edge-complement. This operation induces an equivalence relation on graphs; determining the size of the resulting…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…