Perfect graphs, by definition, have a nice structure, that graph searching seems to extract in a, often non-inexpensive, manner. We scratch the surface of this elegant research area by giving two examples: Lexicographic Breadth Search on Chordal Graphs, and Lexicographic Depth First Search on Cocomparability graphs.

A lexicographic ranking function for the set of all permutations of n ordered symbols translates permutations to their ranks in the lexicographic order of all permutations. This is frequently used for indexing data structures by permutations. We present algorithms for computing both the ranking function and its inverse using O(n) arithmetic operations.

In the context of combinatorial sampling, so-called “unranking method” can be seen as a link between total order over objects and an effective way to construct object given rank. The most classical used in this is lexicographic order, which corresponds familiar word ordering dictionary. article, we propose comparative study four algorithms dedicated unranking combinations, including three that ...

Simulation optimization is an approach that is used to solve problems involving stochastic components. This paper presents a Lexicographic Nelder–Mead (LNM) based simulation optimization (LNM-SO) method to solve multi-criteria simulation optimization problems. The method is designed to be relatively easy-to-implement and be applicable to a wide range of problem domains. To effectively evaluate ...