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...

The complete graph on n vertices is denoted by K, and the graph on n vertices in which each pair of vertices is joined by exactly 2 edges is denoted by 2K,. An m-cycle is a sequence of m distinct vertices (u1, u2, . . . . u,) such that ui is adjacent to ui+ 1 and U, is adjacent to u1 . A spanning subgraph H of G is a subgraph for which V(H) = V(G). An i-factor of a graph G is a spanning subgrap...

Edge detection is one of the most commonly used operations in image analysis, and there are more algorithms in the literature for enhancing and detecting edges. Natural images contain both textured and untextured regions, so the cues of contour and texture are exploited simultaneously. In this paper, we present a new edge detection method for natural images using decomposition model. The main i...

A geometry in Oracle Spatial can be one of the following1: • Point • Linestring connecting two or more points • Polygon specified as a closed linestring and indicating an area bounded by the linestring (with zero or more holes inside the outer bounding linestring) • Multipoint collection • Multiline collection consisting of unconnected linestrings • Multipolygon collection consisting of nonover...

Given a graph G and a subset W ⊆ V (G), a Steiner W -tree is a tree of minimum order that contains all of W . Let S(W ) denote the set of all vertices in G that lie on some Steiner W -tree; we call S(W ) the Steiner interval of W . If S(W ) = V (G), then we call W a Steiner set of G. The minimum order of a Steiner set of G is called the Steiner number of G. Given two vertices u, v in G, a short...

A decomposition of λ copies of monochromatic Kv into copies of K4 such that each copy of K4 contains at most one edge from each Kv is called a proper edge coloring of a BIBD(v, 4, λ). We show that the necessary conditions are sufficient for the existence of a BIBD(v, 4, λ) which has such a proper edge coloring.

A ~ P3-decomposition of a directed graph D is a partition of the arcs of D into directed paths of length 2. We characterize symmetric digraphs that do not admit a ~ P3-decomposition. We show that the only 2-regular, connected directed graphs that do not admit a ~ P3-decomposition are obtained from undirected odd cycles by replacing each edge by two oppositely directed arcs. In both cases, we gi...

Motivated by hypergraph decomposition algorithms, we introduce the notion of edge-induced vertex-cuts and compare it with the well-known notions of edge-cuts and vertex-cuts. We investigate the complexity of computing minimum edge-induced vertex-cuts and demonstrate the usefulness of our notion by applications in network reliability and constraint satisfaction.

Motivated by hypergraph decomposition algorithms, we introduce the notion of edge-induced vertex-cuts and compare it with the well-known notions of edge-cuts and vertex-cuts. We investigate the complexity of computing minimum edge-induced vertex-cuts and demonstrate the usefulness of our notion by applications in network reliability and constraint satisfaction.

A graph of small branchwidth admits efficient dynamic programming algorithms for many NP-hard problems on the graph. A key step in these algorithms is to find a branch decomposition of small width for the graph. Given a planar graph G of n vertices, an optimal branch decomposition of G can be computed in polynomial time, e.g., by the edge-contraction method in O(n) time. All known algorithms fo...