Approximating the discrete time-cost tradeoff problem with bounded depth

11/04/2020
by   Siad Daboul, et al.
0

We revisit the deadline version of the discrete time-cost tradeoff problem for the special case of bounded depth. Such instances occur for example in VLSI design. The depth of an instance is the number of jobs in a longest chain and is denoted by d. We prove new upper and lower bounds on the approximability. First we observe that the problem can be regarded as a special case of finding a minimum-weight vertex cover in a d-partite hypergraph. Next, we study the natural LP relaxation, which can be solved in polynomial time for fixed d and – for time-cost tradeoff instances – up to an arbitrarily small error in general. Improving on prior work of Lovász and of Aharoni, Holzman and Krivelevich, we describe a deterministic algorithm with approximation ratio slightly less than d/2 for minimum-weight vertex cover in d-partite hypergraphs for fixed d and given d-partition. This is tight and yields also a d/2-approximation algorithm for general time-cost tradeoff instances. We also study the inapproximability and show that no better approximation ratio than d+2/4 is possible, assuming the Unique Games Conjecture and P≠NP. This strengthens a result of Svensson, who showed that under the same assumptions no constant-factor approximation algorithm exists for general time-cost tradeoff instances (of unbounded depth). Previously, only APX-hardness was known for bounded depth.

READ FULL TEXT

page 1

page 16

page 18

research
08/30/2018

Improved approximation algorithms for hitting 3-vertex paths

We study the problem of deleting a minimum cost set of vertices from a g...
research
01/30/2023

Faster Algorithm for Minimum Ply Covering of Points with Unit Squares

Biedl et al. introduced the minimum ply cover problem in CG 2021 followi...
research
09/08/2019

Target Set Selection for Conservative Populations

Let G = (V,E) be a graph on n vertices, where d_v denotes the degree of ...
research
08/17/2018

Optimal Distributed Weighted Set Cover Approximation

We present a time-optimal deterministic distributed algorithm for approx...
research
11/25/2022

Simple Algorithms for Stochastic Score Classification with Small Approximation Ratios

We revisit the Stochastic Score Classification (SSC) problem introduced ...
research
08/05/2021

Bifactor Approximation for Location Routing with Vehicle and Facility Capacities

Location Routing is a fundamental planning problem in logistics, in whic...
research
04/11/2018

A PTAS for Euclidean TSP with Hyperplane Neighborhoods

In the Traveling Salesperson Problem with Neighborhoods (TSPN), we are g...

Please sign up or login with your details

Forgot password? Click here to reset