The input is a bipartite graph G = (A ∪B ,E) where each vertex u ∈ A ∪B ranks its neighbors in a strict order of preference. This is the same as an instance of the stable marriage problem with incomplete lists. A matching M∗ is said to be popular if there is no matching M such that more vertices are better off in M than in M∗. Any stable matching of G is popular, however such a matching is a mi...

Due to the overlapped region and image size of the input image pair is unpredictable, it makes the matching procedure more difficult and unstable. For the purpose of finding out the stable and accurate matching algorithm of large images, we give an analysis of different kinds of characters, such as, scale invariant feature transform (SIFT), local maximum gradient descriptor, Harris corners, and...

A geometric graph is a graph whose vertex set is a set of points in the plane and whose edge set contains straight-line segments. A matching in a graph is a subset of edges of the graph with no shared vertices. A matching is called perfect if it matches all the vertices of the underling graph. A geometric matching is a matching in a geometric graph. In this thesis, we study matching problems in...

As far as we know, for most polynomially solvable network optimization problems, their inverse problems under l1 or l∞ norm have been studied, except the inverse maximum-weight matching problem in non-bipartite networks. In this paper we discuss the inverse problem of maximum-weight perfect matching in a non-bipartite network under l1 and l∞ norms. It has been proved that the inverse maximum-we...

This paper first reviews some theoretical results in errortolerant graph matching that were obtained recently. The results include a new metric for error-tolerant graph matching based on maximum common subgraph, a relation between maximum common subgraph and graph edit distance, and the existence of classes of cost functions for error-tolerant graph matching. Then some new optimal algorithms fo...