TY - GEN

T1 - Algorithms and adaptivity gaps for stochastic probing

AU - Gupta, Anupam

AU - Nagarajan, Viswanath

AU - Singla, Sahil

N1 - Publisher Copyright:
© (2016) by SIAM: Society for Industrial and Applied Mathematics.

PY - 2016

Y1 - 2016

N2 - A stochastic probing problem consists of a set of elements whose values are independent random variables. The algorithm knows the distributions of these variables, but not the actual outcomes. The only way to learn the actual outcomes is to probe these elements. However, there are constraints on which set of elements may be probed. (E.g., we may have to travel in some metric to probe elements but have limited time.) These constraints are called outer constraints. We want to develop an algorithm that picks some set of elements to maximize the (expected) value, subject to the picked subset of elements satisfying some other set of constraints, called the inner constraints. In the past, probing problems were studied for the case when both inner and outer constraints were intersections of matroids; these modeled kidney matching and Bayesian auctions applications. One limitation of past work was their reliance on linear-programming-like techniques, which made going beyond matroid-like structures difficult. In this work, we give a very general adaptivity gap result that holds for all prefix-closed outer constraints, as long as the inner constraints are intersections of matroids. The adaptivity gap is O(logn) for any constant number of inner matroid constraints. The prefix-closedness captures most "reasonable" outer constraints, like orienteering, connectivity, and precedence. Based on this we obtain the first approximation algorithms for a number of stochastic probing problems, which have applications, e.g., to path-planning and precedence-constrained scheduling.

AB - A stochastic probing problem consists of a set of elements whose values are independent random variables. The algorithm knows the distributions of these variables, but not the actual outcomes. The only way to learn the actual outcomes is to probe these elements. However, there are constraints on which set of elements may be probed. (E.g., we may have to travel in some metric to probe elements but have limited time.) These constraints are called outer constraints. We want to develop an algorithm that picks some set of elements to maximize the (expected) value, subject to the picked subset of elements satisfying some other set of constraints, called the inner constraints. In the past, probing problems were studied for the case when both inner and outer constraints were intersections of matroids; these modeled kidney matching and Bayesian auctions applications. One limitation of past work was their reliance on linear-programming-like techniques, which made going beyond matroid-like structures difficult. In this work, we give a very general adaptivity gap result that holds for all prefix-closed outer constraints, as long as the inner constraints are intersections of matroids. The adaptivity gap is O(logn) for any constant number of inner matroid constraints. The prefix-closedness captures most "reasonable" outer constraints, like orienteering, connectivity, and precedence. Based on this we obtain the first approximation algorithms for a number of stochastic probing problems, which have applications, e.g., to path-planning and precedence-constrained scheduling.

UR - http://www.scopus.com/inward/record.url?scp=84963537597&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84963537597&partnerID=8YFLogxK

U2 - 10.1137/1.9781611974331.ch120

DO - 10.1137/1.9781611974331.ch120

M3 - Conference contribution

AN - SCOPUS:84963537597

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1731

EP - 1747

BT - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016

A2 - Krauthgamer, Robert

PB - Association for Computing Machinery

T2 - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016

Y2 - 10 January 2016 through 12 January 2016

ER -