Orienteering with One Endomorphism

Endomorphism Spectrums and Endomorphism Types of Graphs

In this paper, the endomorphisms, the half-strong endomorphisms, the locally strong endomorphisms, the quasi-strong endomorphisms, the strong endomorphisms and the automorphisms of a join of cycle n C and a vertex y are investigated. Some enumerative problems concerning these graphs are solved. In particular, the endomorphism spectrums and the endomorphism types of these graphs are given. It ha...

On graphs with a given endomorphism monoid

Program Orienteering

The orienteering problem with variable profits

This paper introduces, models and solves a generalization of the Orienteering Problem, called the The Orienteering Problem with Variable Profits (OPVP). The OPVP is defined on a complete undirected graph G = (V,E), with a depot at vertex 0. Every vertex i ∈ V \ {0} has a profit pi to be collected, and an associated collection parameter αi ∈ [0, 1]. The vehicle may make a number of “passes”, col...

Team Orienteering Problem with Decreasing Profits

Team Orienteering with Decreasing Profits (DP-TOP) extends the classical Team Orienteering problem (TOP) by considering the profit of each client as a decreasing function of time. It consists of maximizing the sum of collected profit by a fixed number K of vehicles, visiting each client at most once. In this work, we present lower bounds based on a Dantzig-Wolfe decomposition and column generat...