Paths, Trees, and Minimum Latency Tours

A Study of Algorithms for Minimum Latency Problem and Online Job Scheduling

We study two problems namely the Minimum Latency Problem (aka the travelling repairman problem) and the Machine Minimization Problem in online job scheduling. The Minimum latency problem is known to be NP-hard even when restricted to weighted trees. The problem has been shown to have PTAS for weighted trees and graphs with a Eucledian metric. We also investigate the problem for caterpillar grap...

Minimum Latency Tours and the k-Traveling Repairmen Problem

Optimal random matchings, tours, and spanning trees in hierarchically separated trees

We derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size n distributed among the leaves of a balanced hierarchically separated tree. We consider monochromatic and bichromatic versions of the minimum matching, minimum spanning tree, and traveling salesman problems. We also present tight concentration results for the monochromatic...

Exact algorithms for the minimum latency problem

Let G = (V, E,w) be an undirected graph with positive weight w(e) on each edge e ∈ E. Given a starting vertex s ∈ V and a subset U ⊂ V as the demand vertex set, the minimum latency problem (MLP) asks for a tour P starting at s and visiting each demand vertex at least once such that the total latency of all demand vertices is minimized, in which the latency of a vertex is the length of the path ...

Dynamic trees as search trees via Euler tours, applied to the network simplex algorithm

The dynamic tree is an abstract data type that allows the maintenance of a collection of trees subject to joining by adding edges (linking) and splitting by deleting edges (cutting), while at the same time allowing reporting of certain combinations of vertex or edge values. For many applications of dynamic trees, values must be combined along paths. For other applications, values must be combin...