Shlomi Rubinstein

Approximation algorithms for maximum dispersion

We describe approximation algorithms with bounded performance guarantees for the following problem: A graph is given with edge weights satisfying the triangle inequality, together with two numbers k and p. Find k disjoint subsets of p vertices each, so that the total weight of edges within subsets is maximized

Better approximations for max TSP

We combine two known polynomial time approximation algorithms for the maximum traveling salesman problem to obtain a randomized algorithm which outputs a solution with expected value of at least r times the optimal one for any given r<25/33 .

Approximations for the maximum acyclic subgraph problem

Abstract Given a directed graph G = (V,A), the maximum acyclic subgraph problem is to compute a subset, A′, of arcs of maximum size or total weight so that G′ = (V,A′) is acyclic. We discuss several approximation algorithms for this problem. Our main result is an O(|A| + d3max) algorithm that produces a solution with at least a fraction 1 2 +ω( 1 d max ) of the number of arcs in an optimal solution. Here, dmax is the maximum vertex degree in G.

An approximation algorithm for maximum triangle packing

We present a randomized (89/169 - e)-approximation algorithm for the weighted maximum triangle packing problem, for any given e > 0. This is the first algorithm for this problem whose performance guarantee is better than ½. The algorithm also improves the best-known approximation bound for the maximum 2-edge path packing problem.

A 7/8-approximation algorithm for metric Max TSP

Abstract We present a randomized approximation algorithm for the metric version of undirected Max TSP. Its expected performance guarantee approaches 8 as n→∞, where n is the number of vertices in the graph.

Robust Matchings

We consider complete graphs with nonnegative edge weights. A p-matching is a set of p disjoint edges. We prove the existence of a maximal (with respect to inclusion) matching M that contains for any

An approximation algorithm for the maximum traveling salesman problem

p\le|M|

On the complexity of the k-customer vehicle routing problem

p

An Approximation Algorithm for Maximum Triangle Packing

edges whose total weight is at least