The Price of Information in Combinatorial Optimization

11/01/2017
by   Sahil Singla, et al.
0

Consider a network design application where we wish to lay down a minimum-cost spanning tree in a given graph; however, we only have stochastic information about the edge costs. To learn the precise cost of any edge, we have to conduct a study that incurs a price. Our goal is to find a spanning tree while minimizing the disutility, which is the sum of the tree cost and the total price that we spend on the studies. In a different application, each edge gives a stochastic reward value. Our goal is to find a spanning tree while maximizing the utility, which is the tree reward minus the prices that we pay. Situations such as the above two often arise in practice where we wish to find a good solution to an optimization problem, but we start with only some partial knowledge about the parameters of the problem. The missing information can be found only after paying a probing price, which we call the price of information. What strategy should we adopt to optimize our expected utility/disutility? A classical example of the above setting is Weitzman's "Pandora's box" problem where we are given probability distributions on values of n independent random variables. The goal is to choose a single variable with a large value, but we can find the actual outcomes only after paying a price. Our work is a generalization of this model to other combinatorial optimization problems such as matching, set cover, facility location, and prize-collecting Steiner tree. We give a technique that reduces such problems to their non-price counterparts, and use it to design exact/approximation algorithms to optimize our utility/disutility. Our techniques extend to situations where there are additional constraints on what parameters can be probed or when we can simultaneously probe a subset of the parameters.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/21/2019

The Markovian Price of Information

Suppose there are n Markov chains and we need to pay a per-step price to...
research
10/11/2020

Approximation Algorithms for Stochastic Minimum Norm Combinatorial Optimization

Motivated by the need for, and growing interest in, modeling uncertainty...
research
09/07/2020

Probabilistic analysis of algorithms for cost constrained minimum weighted combinatorial objects

We consider cost constrained versions of the minimum spanning tree probl...
research
11/06/2019

Algorithms and Adaptivity Gaps for Stochastic k-TSP

Given a metric (V,d) and a root∈ V, the classic k-TSP problem is to find...
research
02/12/2011

Multicriteria Steiner Tree Problem for Communication Network

This paper addresses combinatorial optimization scheme for solving the m...
research
02/28/2023

Algorithmic Solutions for Maximizing Shareable Costs

This paper addresses the optimization problem to maximize the total cost...
research
09/27/2015

An intelligent extension of Variable Neighbourhood Search for labelling graph problems

In this paper we describe an extension of the Variable Neighbourhood Sea...

Please sign up or login with your details

Forgot password? Click here to reset