Total Vertex-Irregularity Labelings for Subdivision of Several Classes of Trees

AbstractMotivated by the notion of the irregularity strength of a graph introduced by Chartrand et al. [3] in 1988 and various kind of other total labelings, Baca et al. [1] introduced the total vertex irregularity strength of a graph.In 2010, Nurdin, Baskoro, Salman and Gaos[5] determined the total vertex irregularity strength for various types of trees, namely complete k–ary trees, a subdivision of stars, and subdivision of particular types of caterpillars. In other paper[6], they conjectured that the total vertex irregularity strength of any tree T is only determined by the number of vertices of degree 1, 2, and 3 in T . In this paper, we attempt to verify this conjecture by considering a subdivision of several types of trees, namely caterpillars, firecrackers, and amalgamation of stars

Randomized approximation algorithms : facility location, phylogenetic networks, Nash equilibria

Despite a great effort, researchers are unable to find efficient algorithms for a number of natural computational problems. Typically, it is possible to emphasize the hardness of such problems by proving that they are at least as hard as a number of other problems. In the language of computational complexity it means proving that the problem is complete for a certain class of problems. For optimization problems, we may consider to relax the requirement of the outcome to be optimal and accept an approximate (i.e., close to optimal) solution. For many of the problems that are hard to solve optimally, it is actually possible to efficiently find close to optimal solutions. In this thesis, we study algorithms for computing such approximate solutions