A rounding algorithm for approximating minimum Manhattan networks1

A Rounding Algorithm for Approximating Minimum Manhattan Networks

For a set T of n points (terminals) in the plane, a Manhattan network on T is a network N(T ) = (V,E) with the property that its edges are horizontal or vertical segments connecting points in V ⊇ T and for every pair of terminals, the network N(T ) contains a shortest l1-path between them. A minimum Manhattan network on T is a Manhattan network of minimum possible length. The problem of finding...

Approximating a Minimum Manhattan Network

Approximating Minimum Manhattan Networks

Given a set S of n points in the plane, we deene a Manhattan Network on S as a rectilinear network G with the property that for every pair of points in S, the network G contains the shortest rectilinear path between them. A Minimum Manhattan Network on S is a Manhattan network of minimum possible length. A Manhattan network can be thought of as a graph G = (V; E), where the vertex set V corresp...

Improved Performance of the Greedy Algorithm for the Minimum Set Cover and Minimum Partial Cover Problems

We establish signiicantly improved bounds on the performance of the greedy algorithm for approximating minimum set cover and minimum partial cover. Our improvements result from a new approach to both problems. In particular, (a) we improve the known bound on the performance ratio of the greedy algorithm for general covers without cost, showing that it diiers from the classical harmonic bound by...

Approximating Minimum Linear Ordering Problems

This paper addresses the Minimum Linear Ordering Problem (MLOP): Given a nonnegative set function f on a finite set V , find a linear ordering on V such that the sum of the function values for all the suffixes is minimized. This problem generalizes well-known problems such as the Minimum Linear Arrangement, Min Sum Set Cover, Minimum Latency Set Cover, and Multiple Intents Ranking. Extending a ...