Related papers: Graph Matching: Relax at Your Own Risk
Graph matching is a fruitful area in terms of both algorithms and theories. In this paper, we exploit the degree information, which was previously used only in noiseless graphs and perfectly-overlapping Erd\H{o}s--R\'enyi random graphs…
This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…
We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show…
We consider the problem of identifying a maximum clique in a given graph. We have proposed a mathematical model for this problem. The model resembles the matrix decomposition of the adjacency matrix of a given graph. The objective function…
Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the computer…
Motivated by the classic Generalized Assignment Problem, we consider the Graph Balancing problem in the presence of orientation costs: given an undirected multi-graph G = (V,E) equipped with edge weights and orientation costs on the edges,…
For a given graph $\mathcal{G}$ of order $n$ with $m$ edges, and a real symmetric matrix associated to the graph, $M\left(\mathcal{G}\right)\in\mathbb{R}^{n\times n}$, the interlacing graph reduction problem is to find a graph…
We consider the following stochastic optimization problem first introduced by Chen et al. in \cite{chen}. We are given a vertex set of a random graph where each possible edge is present with probability p_e. We do not know which edges are…
We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, including the (conditional) graph entropy, rate-distortion functions and…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…
An isomorphism between two graphs is a bijection between their vertices that preserves the edges. We consider the problem of determining whether two finite undirected weighted graphs are isomorphic, and finding an isomorphism relating them…
In modern data analysis, one is frequently faced with statistical inference problems involving massive datasets. Processing such large datasets is usually viewed as a substantial computational challenge. However, if data are a…
A general novel approach mapping discrete, combinatorial, graph-theoretic problems onto ``physical'' models - namely $n$ simplexes in $n-1$ dimensions - is applied to the graph equivalence problem. It is shown to solve this long standing…
We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein…
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,…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
We consider heuristic algorithm for solving graph isomorphism problem. The algorithm based on a successive splitting of the eigenvalues of the matrices which are modifications (to positive defined) of graphs' adjacency matrices.…
The graph isomorphism (GI) problem, which asks whether two graphs are structurally identical, occupies a unique position in computational complexity -- it is neither known to be solvable in polynomial time, nor proven to be NP-complete. We…