Let G = (V, E) be a graph and a weight function w : E -+ Z+. Let T C V be an even subset of the vertices of G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. A T-join is a minimal subset of edges that meets every T-cut (a generalization of solutionS to the Chinese postman problem). The main theorem of this paper gives a tight upper bound on the difference between the ...

This paper describes methods aimed at increasing the eeciency of cutset-based assembly sequence planners by: (i) providing an alternative representation to precedence constraints which is easy to maintain and facilitates the logical evaluation of assembly operations, (ii) maximizing the reuse of previous results of assembly operation feasibility evaluations and (iii) using exact and heuristic a...

Let T be an even subset of the vertices of a graph G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. We prove that if G is bipartite, then the maximum number of disjoint !T-cuts is equal to the minimum cardinality of a set of edges which meets every T-cut. (A weaker form of this was proved by Edmonds and Johnson.) We deduce a solution to the real-valued multi-commodit...

Many divide-and-conquer algorithms on graphs are based on finding a small set of vertices or edges whose removal divides the graph roughly in half. Applications include VLSI layouts [14], Gaussian elimination Cl.51 and graph embeddings [17]. Formally, a class of graphs hasf’(n) vertex (edge) separator if every n-vertex graph in the class has a vertex (edge) cutset of sizef(n) that divides the g...

A (δ, g)-cage is a regular graph of degree δ and girth g with the least possible number of vertices. It was proved by Fu, Huang and Rodger that every (3, g)-cage is 3-connected. Moreover, the same authors conjectured that all (δ, g)-cages are δ-connected for every δ ≥ 3. As a first step towards the proof of this conjecture, Jiang and Mubayi showed that every (δ, g)-cage with δ ≥ 3 is 3-connecte...

The edge-tenacity Te(G) of a graph G was defined as Te(G) = min F⊂E(G) {| F | +τ(G− F ) ω(G− F ) } where the minimum is taken over all edge cutset F of G. We define G-F to be the graph induced by the edges of E(G) − F , τ(G − F ) is the number of edges in the largest component of the graph induced by G-F and ω(G−F ) is the number of components of G− F . A set F ⊂ E(G) is said to be a Te-set of ...

Controlled islanding is considered to be the last countermeasure to prevent system-wide blackouts in case of cascading failures. It splits the system into self-sustained islands to maintain transient stability at the expense of possible loss of load. Generator coherence identification is critical to controlled islanding scheme as it helps identify the optimal cutset to maintain system transient...

In this paper, we present an eecient Iterative Improvement based Partitioning (IIP) algorithm called LSR/MFFS, that combines signal ow based Maximum Fanout Free Sub-graph (MFFS) clustering algorithm with Loose and Stable net Removal (LSR) partitioning algorithm. The MFFS algorithm generalizes existing MFFC decomposition method from combinational circuits to general sequential circuits in order ...

Constraint satisfaction problems are NP-complete in general, but they can be solved in polynomial time and also in parallel if their associated hypergraph is acyclic. It is often important for applications to solve also non-acyclic problems, thus finding larger tractable classes of CSPs is of high interest. Many structural decomposition methods have been suggested, which enable that the efficie...

We investigate various notions of sobriety for topological spaces that are equivalent in ZF set theory with the Axiom of Choice but may differ in the absence of choice principles. The Ultrafilter Principle UP (alias Prime Ideal Theorem) suffices for the desired conclusions. We derive from UP three topological postulates and prove their equivalence in ZF without choice: the Well-Filtration Princ...