Recently there has been extensive work on maintaining (approximate) maximum matchings in dynamic graphs. We consider a generalisation of this problem known as themaximum b-matching: Every node v has a positive integral capacity bv, and the goal is to maintain an (approximate) maximum-cardinality subset of edges that contains at most bv edges incident on every node v. The maximum matching proble...

Scaled Matching refers to the problem of nding all locations in the text where the pattern, proportionally enlarged according to an arbitrary integral scale, appears. Scaled matching is an important problem that was originally inspired by problems in Vision. However, in real life, a more natural model of scaled matching is the Real Scaled Matching model. Real scaled matching is an extended vers...

Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in sparsityrelated techniques. We cast the problem, resembling group or collaborative sparsity formulations, as a non-smooth convex optimization problem that can be efficient...

By prior work, it is known that any distributed graph algorithm finds a maximal matching requires $$\varOmega (\log ^* n)$$ communication rounds, while possible to find fractional in O(1) rounds bounded-degree graphs. However, all O(1)-round algorithms for use arbitrarily fine-grained values. In particular, none of them able half-integral solution, using only values from $$\{0, \frac{1}{2}, 1\}...

A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.

Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...

Image-based localization is an important problem in robotics and an integral part of visual mapping and navigation systems. An approach to robustly match images to previously recorded ones must be able to cope with seasonal changes especially when it is supposed to work reliably over long periods of time. In this paper, we present a novel approach to visual localization of mobile robots in outd...

In this paper we use interior-point methods for linear programming, developed in the context of sequential computation, to obtain a parallel algorithm for the bipartite matching problem. Our algorithm nds a maximum cardinality matching in a bipartite graph with n nodes and m edges in O(pm log3 n) time on a CRCW PRAM. Our results extend to the weighted bipartite matching problem and to the zero-...