This paper presents the application of metaheuristic methods to the minimum crossing number problem for the first time. These algorithms including particle swarm optimization, improved ray optimization, colliding bodies optimization and enhanced colliding bodies optimization. For each method, a pseudo code is provided. The crossing number problem is NP-hard and has important applications in eng...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 26 February 2020Accepted: 15 March 2021Published online: 01 June 2021Keywordsindependence number, bounded maximum degree, bipartite extremal problemsAMS Subject Headings05C35, 05D40Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society for Indus...

pointing towards the sensor and a i is a binary number depending on the intersection of l and Q i , and The reason behind taking a weighted sum of the intersection points is that the sensor measurement of the position of a surface point is less reliable if the local surface is facing away from the sensor. The weight w i is a reflection of this heuristic. In general, the sensor direction informa...

By using the notion of compatibility of subgraphs with a perfect matching developed for digraphs in [1], we show that if, in a balanced bipartite graph G of minimum degree 6, the maximum cardinality ebip of a balanced independent subset satisfies ~bip ~< 26-4, then G is hamiltonian-biconnected, and if Ctbip ~< 26-2, G contains a hamiltonian path. Moreover, we give some properties of balanced bi...

Tolerance graphs have been extensively studied since their introduction in 1982 [9], due to their interesting structure and their numerous applications, as they generalize both interval and permutation graphs in a natural way. It has been conjectured in 1984 that the intersection of tolerance and cocomparability graphs coincides with bounded tolerance graphs [10]. The conjecture has been proved...