We show that the problem of guarding an x-monotone terrain from an altitude line and the problem of guarding a uni-monotone polygon are equivalent. We present a polynomial time algorithm for both problems, and show that the cardinality of a minimum guard set and the cardinality of a maximum witness set coincide. Thus, uni-monotone polygons are perfect; this result also extends to monotone mount...

nowadays we are living in a situation that houses are looked as a profitable product and as an economic need for families, instead of being a place for tranquillity. in the other word, home which is generally a place of residence is now replaced by shelter. in the other hand, people need to have tranquillity, sense of security in private life and respected territory; so organization of living e...

Density has been suggested to affect variation in extra-pair paternity (EPP) in avian mating systems, because increasing density promotes encounter rates and thus mating opportunities. However, the significance of density affecting EPP variation in intra- and interspecific comparisons has remained controversial, with more support from intraspecific comparisons. Neither experimental nor empirica...

This paper discusses a distance guarding concept on triangulation graphs, which can be associated with distance domination and distance vertex cover. We show how these subjects are interconnected and provide tight bounds for any n-vertex maximal outerplanar graph: the 2d-guarding number, g2d(n) = ⌊ n 5 ⌋; the 2d-distance domination number, γ2d(n) = ⌊ n 5 ⌋; and the 2d-distance vertex cover numb...

In this extended abstract, we first present a PTAS for guarding the vertices of a weakly-visible polygon P from a subset of its vertices, or in other words, a PTAS for computing a minimum dominating set of the visibility graph of the vertices of P . We then show how to obtain a PTAS for vertex guarding the entire polygon. Digital Object Identifier 10.4230/LIPIcs...