In this paper we relate antiblocker duality between polyhedra, graph theory and the disjunctive procedure. In particular, we analyze the behavior of the disjunctive procedure over the clique relaxation, K(G), of the stable set polytope in a graph G and the one associated to its complementary graph, K(Ḡ). We obtain a generalization of the Perfect Graph Theorem proving that the disjunctive indice...

Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.

We study the maximum flow problem subject to binary disjunctive constraints in a directed graph: A negative disjunctive constraint states that a certain pair of arcs in a digraph cannot be simultaneously used for sending flow in a feasible solution. In contrast to this, positive disjunctive constraints force that for certain pairs of arcs at least one arc has to carry flow in a feasible solutio...

For a graph G = (V,E), a set D ⊆ V is called a disjunctive dominating set of G if for every vertex v ∈ V \D, v is either adjacent to a vertex of D or has at least two vertices in D at distance 2 from it. The cardinality of a minimum disjunctive dominating set of G is called the disjunctive domination number of graph G, and is denoted by γ 2 (G). The MINIMUM DISJUNCTIVE DOMINATION PROBLEM (MDDP)...

We study the minimum spanning tree problem, the maximum matching problem and the shortest path problem subject to binary disjunctive constraints: A negative disjunctive constraint states that a certain pair of edges cannot be contained simultaneously in a feasible solution. It is convenient to represent these negative disjunctive constraints in terms of a so-called conflict graph whose vertices...

One of the major hurdles to implementing a practical disjunctive database is the CoNP-completeness of executing queries. We demonstrate, however, that this problem is similar to the problem of computing the transitive closure of a node in a disjunctive graph. While this problem is also CoNP-complete in general, we show in this paper that there is a polynomial-time solution that solves it for ce...

in this paper, the flexible job shop scheduling problem with machine flexibility and controllable process times is studied. the main idea is that the processing times of operations may be controlled by consumptions of additional resources. the purpose of this paper to find the best trade-off between processing cost and delay cost in order to minimize the total costs. the proposed model, flexibl...

Solvers for Answer Set Programming Marco Maratea Universita’ degli Studi di Genova, Italy (e-mail: [email protected]) Abstract Abstract solvers are a recently employed method to formally describe, compare and combine solving algorithms, where the states of computation are represented as nodes of a graph, the solving techniques as edges between such nodes, the solving process as a path in the ...

In the literature of the combinatorial optimization problems, it is a commonplace to find more than one mathematical model for the same problem. The significance of a model may be measured in terms of the efficiency of the solution algorithms that can be built upon it. The purpose of this article is to present a new network model for the well known combinatorial optimization problem – the job s...

It is known that bottom-up query evaluation can be extended to work with disjunctive facts, but there seems to be the common assumption that it is much too ineecient for practical applications. In this paper, we improve the extended bottom-up evaluation by making the resolvable literal in a disjunctive fact unique. In many cases, this reduces an exponential behaviour to a polynomial one. We int...