The traveling–salesman problem (TSP) is one of the most studied problems in combinatorial optimization [16, 14]. The TSP is simply stated, has practical applications, and is a representative of a large class of important scientific and engineering problems. The TSP can be viewed as a graph–theory problem if the cities are identified with the vertices of a graph, and the links between the cities...

This paper proposes an efficient algorithm to evaluate system reliability for many real-life systems such as manufacturing, telecommunication and computers systems. A multicommodity stochastic-flow network is constructed to model a manufacturing system in which each node stands for a machine station, and each arc stands for a transmission medium (shipping machine or conveyor). Four characterist...

A circular-arc graph is the intersection graph of arcs of a circle. A Helly circular-arc graph is a circular-arc graph admitting a model whose arcs satisfy the Helly property. A clique-independent set of a graph is a set of pairwise disjoint cliques of the graph. It is NP-hard to compute the maximum cardinality of a clique-independent set for a general graph. In the present paper, we propose al...

A noneven digraph is a directed graph with self-loops such that at least one weight-ing of its arcs by 0 or 1 results in no even cycles. A directed cycle in a weighted digraph is even if the sum of weights of its arcs is an even number. The characterisation of 2-connected undirected graphs G such that their symmetric directed counterparts G are noneven, is obtained via a result of Kastelyn conc...

We present a fast local search algorithm that finds an improved solution (if there is any) in the k-exchange neighborhood of the given solution to an instance of WEIGHTED FEEDBACK ARC SET IN TOURNAMENTS. More precisely, given an arc weighted tournament T on n vertices and a feedback arc set F (a set of arcs whose deletion from T turns it into a directed acyclic graph), our algorithm decides in ...

We present a fast local search algorithm that finds an improved solution (if there is any) in the k-exchange neighborhood of the given solution to an instance of WEIGHTED FEEDBACK ARC SET IN TOURNAMENTS. More precisely, given an arc weighted tournament T on n vertices and a feedback arc set F (a set of arcs whose deletion from T turns it into a directed acyclic graph), our algorithm decides in ...

The problem of computing performability probabilities in stochastic PERT and ow networks is studied when the network is \minimally designed" to withstand any two component failures. Polynomial-time algorithms to compute performability when the network is planar| the nonplanar versions being NP-hard | solve related \two-path subset" problems. Given an acyclic graph with weights on the arcs, the ...

In the Mixed Chinese Postman Problem (MCPP), given a weighted mixed graph G (G may have both edges and arcs), our aim is to find a minimum weight closed walk traversing each edge and arc at least once. The MCPP parameterized by the number of edges in G or the number of arcs in G is fixed-parameter tractable as proved by van Bevern et al. (in press) and Gutin, Jones and Sheng (ESA 2014), respect...

It is still debated whether the low-doping Fermi surface of cuprates composed hole pockets or disconnected arcs. Results from cellular dynamical mean field theory (c-DMFT) support arcs hypothesis by predicting corresponding for Hubbard model. Here, we introduce a simple parametrization self-energy, in spirit Yang-Rice-Zhang theory, and show that state art c-CDMFT calculations cannot give defini...