Generalizing the cost in the standard min-cut problem to a submodular cost function immediately makes the problem harder. Not only do we prove NP hardness even for nonnegative submodular costs, but also show a lower bound of Ω(|V |) on the approximation factor for the (s, t) cut version of the problem. On the positive side, we propose and compare three approximation algorithms with an overall a...

We address the following problem: given an undirected graph G = (V,E), with vertex set V of cardinality n and edge set E, where each edge (i, j) has a non-negative integer weight wij , and given a constant B, 0 ≤ B < n, find a cut (S, V \ S) of G of maximum weight such that the difference between the cardinalities of the two shores of the cut is not greater than B. This problem has been introdu...

Proof. We first prove the sufficiency. Since any two vertices of G are connected by two internally disjoint paths, then for each vertex v of G, any two vertices of G − v are connected by at least one path, i.e., c(G − v) = c(G). Hence G has no cut vertex. Next we prove the necessity. Let u, v be two distinct vertices of G. To show that there are internally disjoint paths between u and v, we app...

The variable sum exdeg index of a graph G is defined as $SEI_a(G)=sum_{uin V(G)}d_G(u)a^{d_G(u)}$, where $aneq 1$ is a positive real number,  du(u) is the degree of a vertex u ∈ V (G). In this paper, we characterize the graphs with the extremum variable sum exdeg index among all the graphs having a fixed number of vertices and cut edges, for every a>1.

Energy distribution results from pulsed inductive discharges in Argon and Xenon are presented. Calculations are based on a series RLC circuit analysis of the Missouri Plasmoid Experiment in vacuum and plasma. Initial results show an energy deficit of 16.3 J and 15.9 J for Argon and Xenon, respectfully, for a 10 mTorr pre-fill with 79.5 J initial stored energy. At 100 mTorr, the deficits increas...

OBJECTIVE Seed filling in view lattice is a method for accelerating volume rendering. Our previously published results on using seed filling had the limitation that they did not support cut planes. Cut planes are one of the main advantages of using volume rendering over surface rendering. In this article we describe the seed-filling acceleration technique and propose two fast reseeding processe...

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V,E) and the goal is to find a subset of vertices S ⊆ V that maximizes the number of edges in the cut δ(S) such that the induced graph G[S] is connected. We present the first non-trivial Ω( 1 logn ) approximation algorithm for the Connected Maximum Cut problem in general graphs using novel techniques. We then ...

When the chiral limit m → 0 of QCD is taken at finite four-volume V , one will eventually, no matter how big V is, reach a regime where the pion Compton wavelength 1/mπ exceeds the linear size L ≡ V 1/4 of the box. If the volume at the same time is much bigger than the QCD scale, one is in an interesting region, the ǫ-regime of QCD, where the spontaneously broken chiral symmetry is dictating th...