Ant Colony Optimization (ACO) metaheuristic is a multi-agent system in which the behaviour of each ant inspired by foraging real ants to solve optimization problem. Set Covering Problems (SCP), on other hand, deal with maximizing coverage every subset while weight nodes used must be minimized. In this paper, ACO was adapted and case Problem. The for solving SCP implemented as computer program u...

We study three covering problems in the plane. Our original motivation for these come from trajectory analysis. The first is to decide whether a given set of line segments can be covered by up four unit-sized, axis-parallel squares. second build data structure on efficiently answer any query subtrajectory coverable unit-sized third problem compute longest that two

Multigranulation rough set theory is one of the most effective tools for data analysis and mining in multicriteria information systems. Six types covering-based multigranulation fuzzy (CMFRS) models have been constructed through β -neighborhoods or measures. However, it often time-consuming to compute these CMFRS with a ...

Then Γ acts cocompactly on X and X , and the orbit spaces X/Γ and X /Γ are closed manifolds with contractible universal covers. The only nontrivial homotopy groups are thus the fundamental groups, π1(X/Γ) ∼= Γ ∼= π1(X /Γ). It follows that there is a homotopy equivalence X/Γ X /Γ which can be lifted to a map f : X X . This map f can then be shown to be a quasi-isometry. Recall that a (not necess...

This paper presents a simple, efficient algorithm to compute the covering graph of the lattice generated by a family B of subsets of a set X. The implementation of this algorithm has O((|X| + |B|) · |B|) time complexity per lattice element. This improves previous algorithms of Bordat (1986), Ganter and Kuznetsov (1998) and Jard et al. (1994). This algorithm can be used to compute the Galois (co...

In this paper, we study the restriction of an irreducible unitary representation π of the universal covering S̃p2n(R) to a Heisenberg maximal parabolic group P̃ . We prove that if π|P̃ is irreducible, then π must be a highest weight module or a lowest weight module. This is in sharp constrast with the GLn(R) case. In addition, we show that for a unitary highest or lowest weight module, π|P̃ decompo...