This paper presents an alternative approach to the image segmentation problem. Similar to other recent proposals a graph theoretic framework is used: Given an image a weighted undirected graph is constructed, where each pixel becomes a vertex of the graph and edges measure a relationship between pixels. Our approach differs from previous work in the way we define the edge weights. Typically the...

A circuit cover of an edge-weighted graph (G, p) is a multiset of circuits in G such that every edge e is contained in exactly p(e) circuits in the multiset. A nonnegative integer valued weight vector p is admissible if the total weight of any edge-cut is even, and no edge has more than half the total weight of any edge-cut containing it. A graph G has the circuit cover property if (G, p) has a...

Let G = (N, E) be an undirected graph with node set N = { 1 ..... n }, edge set E and edge weights {c(e) : e ~ E}. (If the graph is unweighted, then we assume c(e) = 1 for e E E.) A common problem in circuit board and microchip design, computer program segmentation, floor planning and other layout problems is to partition the node set N into k disjoint subsets Sl ..... Sk of specified sizes ml ...

forest roads are directions in natural habitats that used to transport wood products, secondary forest products and recreation. constructing forest roads causes trees clearing with specified width thus lead to direct or indirect changes in forest ecosystems and forest environment. this study aims to assess the changes of diversity and richness indices in main and secondary forest roads in a par...

For a connected graph G = (V, E), an edge set S ⊆ E is a k-restricted edge cut if G−S is disconnected and every component of G− S has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum k-restricted edge cut. Let ξk(G) = min{|[X, X ]| : |X | = k,G[X ] is connected}. G is λk -optimal if λk(G) = ξk(G). Moreover, G is super-λk ...