The survivable network design (SND) problem seeks a minimum cost robust network configuration that provides a specified number of alternate (edge-disjoint) paths between nodes of the network. For this problem, we present a family of new mixed integer programming formulations whose associated linear programming relaxations can be tighter than that of the usual cutset formulation. The new formula...

List partitions generalize list colourings and list homomorphisms. Each symmetric matrix M over 0; 1; deenes a list partition problem. Diierent choices of the matrix M lead to many well-known graph the-oretic problems including the problem of recognizing split graphs and their generalizations, nding homogeneous sets, joins, clique cutsets, stable cutsets, skew cutsets and so on. We develop tool...

A 2-join is an edge cutset that naturally appears in decomposition of several classes of graphs closed under taking induced subgraphs, such as perfect graphs and claw-free graphs. In this paper we construct combinatorial polynomial time algorithms for finding a maximum weighted clique, a maximum weighted stable set and an optimal coloring for a class of perfect graphs decomposable by 2-joins: t...

For conflict resolution between local coordination modules of distributed agents, synthesized based on inter-agent constraints, two original ideas are proposed. The first is a designer-comprehensible Distributed Constraint Specification Network (DCSN) for describing the constraint relationships among agents. The second is an algorithm using cutset theory for generating, from a given DCSN, an AN...

An overlap representation of a graph G assigns sets to vertices so that vertices are adjacent if and only if their assigned sets intersect with neither containing the other. The overlap number φ(G) (introduced by Rosgen) is the minimum size of the union of the sets in such a representation. We prove the following: (1) An optimal overlap representation of a tree can be produced in linear time, a...

We answer three questions posed in a paper by Babson and Benjamini. They introduced a parameter CG for Cayley graphs G that has significant application to percolation. For a minimal cutset of G and a partition of this cutset into two classes, take the minimal distance between the two classes. The supremum of this number over all minimal cutsets and all partitions is CG. We show that if it is fi...

Most standard approaches to the static analysis of programs, such as the popular worklist method, are first-order methods that inductively annotate program points with abstract values. In [6] we introduced a second-order approach based on Kleene algebra. In this approach, the primary objects of interest are not the abstract data values, but the transfer functions that manipulate them. These ele...

In his seminal paper, Pearl [1986] introduced the notion of Bayesian networks and the first processing algorithm, Belief Propagation (BP), that computes posterior marginals, called beliefs, for each variable when the network is singly connected. The paper provided the foundation for the whole area of Bayesian networks. It was the first in a series of influential papers by Pearl, his students an...