The eccentricity transform associates to each point of a shape the geodesic distance to the points farthest away. This can be used to decompose shapes into parts based on the connectivity of the isoheight lines. The adjacency graph of the obtained decomposition is similar to a Reeb graph and characterizes the topology of the object. Graph pyramids are used to efficiently compute the decompositi...

In 1994 S. McGuinness showed that any greedy clique decomposition of an n-vertex graph has at most ⌊n2/4⌋ cliques (The greedy clique decomposition of a graph, J. Graph Theory 18 (1994) 427-430), where a clique decomposition means a clique partition of the edge set and a greedy clique decomposition of a graph is obtained by removing maximal cliques from a graph one by one until the graph is empt...

Abstract. In this paper, we propose a new algorithm for computing recursive closures. The main idea behind this is tree labeling and graph decomposition, based on which the transitive closure of a directed graph can be computed in O(e⋅b) time and O(n⋅b) space, where n is the number of the nodes of the graph, e is the numbers of the edges, and b is the graph’s breadth. It is a better computation...

Dynamic programming is a method in which the solution to a computational problem is found by combination of already obtained solutions to subproblems. This method can be applied to problems on graphs (nodes connected by edges). The graph of interest must then be broken down into successively smaller parts according to some suitable principle. The thesis studies two graph algebras introduced for...

A Graph G = (V,E) is called k-slim if for every subgraph S = (VS , ES) of G with s = |VS | ≥ k there exists K ⊂ VS , |K| = k, such that the vertices of VS \K can be partitioned into two subsets, A and B, such that |A| ≤ 2 3s and |B| ≤ 2 3s and no edge of ES connects a vertex from A and a vertex from B. k-slim graphs contain, in particular, the graphs with tree-width k. In this paper we give an ...

We will revisit the categorical notion of cospan decompositions of graphs and compare it to the well-known notions of path decomposition and tree decomposition from graph theory. More specifically, we will define several types of cospan decompositions with appropriate width measures and show that these width measures coincide with pathwidth and treewidth. Such graph decompositions of small widt...

We introduce a method of hierarchically decomposing graph optimization problems to obtain approximate solutions with low computation. The method uses a partition on the graph to convert the original problem to a high level problem and several lower level problems. On each level, the resulting problems are in exactly the same form as the original one, so they can be further decomposed. In this w...

Programs commonly maintain multiple linked data structures. Correlations between multiple data structures may often be nonexistent or irrelevant to verifying that the program satisfies certain safety properties or invariants. In this paper, we show how this independence between different (singly-linked) data structures can be utilized to perform shape analysis and verification more efficiently....

A decomposition of a graph G is a set D = {H1, · · · , Hk} of pairwise edge-disjoint subgraphs of G that cover the set of edges of G. If Hi is isomorphic to a fixed graph H, for 1 ≤ i ≤ k, then we say that D is an H-decomposition of G. In this work, we study the case where H is a path of fixed length. For that, we first decompose the given graph into trails, and then we use a disentangling lemm...