TY - GEN

T1 - Towards distributed two-stage stochastic optimization

AU - Emek, Yuval

AU - Harlev, Noga

AU - Izumi, Taisuke

N1 - Publisher Copyright:
© Yuval Emek, Noga Harlev, and Taisuke Izumi; licensed under Creative Commons License CC-BY 23rd International Conference on Principles of Distributed Systems (OPODIS 2019).

PY - 2020/2

Y1 - 2020/2

N2 - The weighted vertex cover problem is concerned with selecting a subset of the vertices that covers a target set of edges with the objective of minimizing the total cost of the selected vertices. We consider a variant of this classic combinatorial optimization problem where the target edge set is not fully known; rather, it is characterized by a probability distribution. Adhering to the model of two-stage stochastic optimization, the execution is divided into two stages so that in the first stage, the decision maker selects some of the vertices based on the probabilistic forecast of the target edge set. Then, in the second stage, the edges in the target set are revealed and in order to cover them, the decision maker can augment the vertex subset selected in the first stage with additional vertices. However, in the second stage, the vertex cost increases by some inflation factor, so the second stage selection becomes more expensive. The current paper studies the two-stage stochastic vertex cover problem in the realm of distributed graph algorithms, where the decision making process (in both stages) is distributed among the vertices of the graph. By combining the stochastic optimization toolbox with recent advances in distributed algorithms for weighted vertex cover, we develop an algorithm that runs in time O(log(∆)/ε), sends O(m) messages in total, and guarantees to approximate the optimal solution within a (3 + ε)-ratio, where m is the number of edges in the graph, ∆ is its maximum degree, and 0 < ε < 1 is a performance parameter.

AB - The weighted vertex cover problem is concerned with selecting a subset of the vertices that covers a target set of edges with the objective of minimizing the total cost of the selected vertices. We consider a variant of this classic combinatorial optimization problem where the target edge set is not fully known; rather, it is characterized by a probability distribution. Adhering to the model of two-stage stochastic optimization, the execution is divided into two stages so that in the first stage, the decision maker selects some of the vertices based on the probabilistic forecast of the target edge set. Then, in the second stage, the edges in the target set are revealed and in order to cover them, the decision maker can augment the vertex subset selected in the first stage with additional vertices. However, in the second stage, the vertex cost increases by some inflation factor, so the second stage selection becomes more expensive. The current paper studies the two-stage stochastic vertex cover problem in the realm of distributed graph algorithms, where the decision making process (in both stages) is distributed among the vertices of the graph. By combining the stochastic optimization toolbox with recent advances in distributed algorithms for weighted vertex cover, we develop an algorithm that runs in time O(log(∆)/ε), sends O(m) messages in total, and guarantees to approximate the optimal solution within a (3 + ε)-ratio, where m is the number of edges in the graph, ∆ is its maximum degree, and 0 < ε < 1 is a performance parameter.

KW - And phrases weighted vertex cover

KW - Distributed graph algorithms

KW - Primal-dual

KW - Two-stage stochastic optimization

UR - http://www.scopus.com/inward/record.url?scp=85081169070&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.OPODIS.2019.32

DO - 10.4230/LIPIcs.OPODIS.2019.32

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AN - SCOPUS:85081169070

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 23rd International Conference on Principles of Distributed Systems, OPODIS 2019

A2 - Felber, Pascal

A2 - Friedman, Roy

A2 - Gilbert, Seth

A2 - Miller, Avery

T2 - 23rd International Conference on Principles of Distributed Systems, OPODIS 2019

Y2 - 17 December 2019 through 19 December 2019

ER -