Improved approximation algorithms for the Min–Max Selecting Items problem

Improved Approximation Algorithms for the Min-Max Selecting Items Problem

We give a simple deterministic O(logK/ log logK) approximation algorithm for the Min-Max Selecting Items problem, where K is the number of scenarios. While our main goal is simplicity, this result also improves over the previous best approximation ratio of O(logK) due to Kasperski, Kurpisz, and Zieliński (Information Processing Letters (2013)). Despite using the method of pessimistic estimators...

Improved Approximation Algorithms for the Matroid Median Problem

We consider the matroid median problem (MMP), which is defined as follows. As in the uncapacitated facility location problem, we are given a set of facilities F and a set of clients D. Each facility i has an opening cost of fi. Each client j ∈ D has demand dj and assigning client j to facility i incurs an assignment cost of djcij proportional to the distance between i and j. Further, we are giv...

Improved Approximation Algorithms for the Capacitated Multicast Routing Problem

For the Capacitated Multicast Routing Problem, we considered two models which are the Multicast k-Path Routing and the Multicast k-Tree Routing. We presented two improved approximation algorithms for them, which have worst case performance ratios of 3 and (2 + ρ) (ρ is the best approximation ratio for the Steiner Tree problem, and is about 1.55), respectively, thus improving upon the previous b...

Improved Approximation Algorithms for the Max-Edge Coloring Problem

The Max Edge-Coloring (MEC) problem is a natural weighted generalization of the classical edgecoloring problem. Formally, in the MEC problem we are given a graph G = (V,E) with a weight function w : E → N , and we ask for a proper edge-coloring of G, M = {M1,M2, . . . ,Mk}, such that the sum of the weights of the heaviest edges in the color classes, W = ∑k i=1max{w(e)|e ∈ Mi}, is minimized. The...

Improved Approximation Algorithms for the Partial Vertex Cover Problem