This paper analyzes decomposition properties of a graph that, when they occur, permit a polynomial solution of the traveling salesman problem and a description of the traveling salesman polytope by a system of linear ...
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This paper analyzes decomposition properties of a graph that, when they occur, permit a polynomial solution of the traveling salesman problem and a description of the traveling salesman polytope by a system of linear equalities and inequalities. The central notion is that of a 3-edge cutset, namely, a set of 3 edges that, when removed, disconnects the graph. Conversely, our approach can be used to construct classes of graphs for which there exists a polynomial algorithm for the traveling salesman problem. The approach is illustrated on two examples, Halin graphs and prismatic graphs.
One of the main issues in flow control problems is deadlock of messages caused by a limited amount of resources. In this paper, the problem of predicting whether a deadlock will necessarily occur in a Store-and-Forwar...
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One of the main issues in flow control problems is deadlock of messages caused by a limited amount of resources. In this paper, the problem of predicting whether a deadlock will necessarily occur in a Store-and-Forward Network is analyzed. We show that, in the case of dynamic routing, the deadlock prediction problem can be decided in polynomial time if tokens are allowed to transit more than once through the same vertex, in contrast with an NP-completeness result in the case where they are allowed to transit at most once.
The Maximum Weight Independent Set Problem (WIS) is a well-known NP-hard problem. A popular way to study WIS is to detect graph classes for which WIS is solvable in polynomial time, with particular reference to heredi...
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The Maximum Weight Independent Set Problem (WIS) is a well-known NP-hard problem. A popular way to study WIS is to detect graph classes for which WIS is solvable in polynomial time, with particular reference to hereditary graph classes, i.e., defined by a hereditary graph property or equivalently by forbidding one or more induced subgraphs. For any two graphs G and H, G + H denotes the disjoint union of G and H. A lK(2) is the disjoint union of l edges. A Y-m,Y-m is the disjoint union of two stars of m + 1 vertices plus one vertex that is adjacent only to the centers of such stars. For any graph family Y, the class of Y-free graphs is formed by graphs which are Y-free for every Y is an element of Y, and the class of lK(2) + Y-free graphs is formed by graph which are lK(2) + Y-free for every Y is an element of Y. The main result of this manuscript is the following: For any constant m and for any graph family Y which contains an induced subgraph of Y-m,Y-m, if WIS is solvable in polynomial time for Y-free graphs, then WIS is solvable in polynomial time for lK(2) + Y-free graphs for any constant l. That extends some known polynomial results, namely, when Y = {Y} and Y is a fork or is a P-5. The proof of the main result is based on Farber's approach to prove that every 2K(2)-free graph has O(n(2)) maximal independent sets (Farber in Discrete Math 73:249-260, 1989), which directly leads to a polynomial time algorithm to solve WIS for 2K(2)-free graphs through a dynamic programming approach, and on some extensions of Farber's approach.
The following case of the classical NP-hard scheduling problem is considered. There is a set of jobs N with identical processing times p = const. All jobs have to be processed on a single machine. The objective functi...
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The following case of the classical NP-hard scheduling problem is considered. There is a set of jobs N with identical processing times p = const. All jobs have to be processed on a single machine. The objective function is minimization of maximum lateness. We analyze algorithms for the makespan problem, presented by Garey et al. (1981) and Simons (1978) and represent two polynomial algorithms to solve the problem and to construct the Pareto set with respect to criteria L max and C max . The complexity of presented algorithms equals O(Q n log n ) and O( n 2 log n ), where 10 - Q is the accuracy of the input-output parameters.
Most existing prevention methods tackle the deadlock issue arising in flexible manufacturing systems modeled with Petri nets by adding monitors and arcs. Instead, this paper presents a new deadlock prevention method b...
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Most existing prevention methods tackle the deadlock issue arising in flexible manufacturing systems modeled with Petri nets by adding monitors and arcs. Instead, this paper presents a new deadlock prevention method based on a characteristic structure of WS 3 PR, an extension of System of Simple Sequential of Processes with Resources (S 3 PR) with weighted arcs. The numerical relationships among weights, and between weights and initial markings are investigated based on simple circuits of resource places, which are the simplest structure of circular wait, rather than siphons. A WS 3 PR satisfying a proposed restriction is inherently deadlock-free and live by configuring its initial markings. A set of polynomial algorithms are developed to implement the proposed method. Several examples are used to illustrate them.
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