DeepAI AI Chat
Log In Sign Up

Constant Factor Approximation Algorithm for Weighted Flow Time on a Single Machine in Pseudo-polynomial time

by   Amit Kumar, et al.

In the weighted flow-time problem on a single machine, we are given a set of n jobs, where each job has a processing requirement p_j, release date r_j and weight w_j. The goal is to find a preemptive schedule which minimizes the sum of weighted flow-time of jobs, where the flow-time of a job is the difference between its completion time and its released date. We give the first pseudo-polynomial time constant approximation algorithm for this problem. The running time of our algorithm is polynomial in n, the number of jobs, and P, which is the ratio of the largest to the smallest processing requirement of a job. Our algorithm relies on a novel reduction of this problem to a generalization of the multi-cut problem on trees, which we call the Demand Multi-Cut problem. Even though we do not give a constant factor approximation algorithm for the Demand Multi-Cut problem on trees, we show that the specific instances of Demand Multi-Cut obtained by reduction from weighted flow-time problem instances have more structure in them, and we are able to employ techniques based on dynamic programming. Our dynamic programming algorithm relies on showing that there are near optimal solutions which have nice smoothness properties, and we exploit these properties to reduce the size of DP table.


page 1

page 2

page 3

page 4


A PTAS for Minimizing Weighted Flow Time on a Single Machine

An important objective in scheduling literature is to minimize the sum o...

A (2+ε)-approximation algorithm for preemptive weighted flow time on a single machine

Weighted flow time is a fundamental and very well-studied objective func...

Simpler constant factor approximation algorithms for weighted flow time – now for any p-norm

A prominent problem in scheduling theory is the weighted flow time probl...

An O(^1.5n n) Approximation Algorithm for Mean Isoperimetry and Robust k-means

Given a weighted graph G=(V,E), and U⊆ V, the normalized cut value for U...

Single Machine Weighted Number of Tardy Jobs Minimization With Small Weights

In this paper we prove new results concerning pseudo-polynomial time alg...

Peak Demand Minimization via Sliced Strip Packing

We study Nonpreemptive Peak Demand Minimization (NPDM) problem, where we...

Approximation algorithms for the MAXSPACE advertisement problem

In the MAXSPACE problem, given a set of ads A, one wants to schedule a s...