TY - GEN

T1 - An LMP O(log n)-approximation algorithm for nodeweighted prize collecting steiner tree

AU - Könemann, Jochen

AU - Sadeghian, Sina

AU - Sanità, Laura

PY - 2013

Y1 - 2013

N2 - In the node-weighted prize-collecting Steiner tree problem (NW-PCST) we are given an undirected graph G = (V,E), non-negative costs c(v) and penalties π(v) for each v ∈ V . The goal is to find a tree T that minimizes the total cost of the vertices spanned by T plus the total penalty of vertices not in T. This problem is well-known to be set-cover hard to approximate. Moss and Rabani (STOC'01) presented a primal-dual Lagrangean-multiplier-preserving O(ln V )-approximation algorithm for this problem. We show a serious problem with the algorithm, and present a new, fundamentally different primal-dual method achieving the same performance guarantee. Our algorithm introduces several novel features to the primal-dual method that may be of independent interest.

AB - In the node-weighted prize-collecting Steiner tree problem (NW-PCST) we are given an undirected graph G = (V,E), non-negative costs c(v) and penalties π(v) for each v ∈ V . The goal is to find a tree T that minimizes the total cost of the vertices spanned by T plus the total penalty of vertices not in T. This problem is well-known to be set-cover hard to approximate. Moss and Rabani (STOC'01) presented a primal-dual Lagrangean-multiplier-preserving O(ln V )-approximation algorithm for this problem. We show a serious problem with the algorithm, and present a new, fundamentally different primal-dual method achieving the same performance guarantee. Our algorithm introduces several novel features to the primal-dual method that may be of independent interest.

KW - Approximation algorithms

KW - Lagrangean multiplier preserving

KW - Node-weighted steiner trees

KW - Prize-collecting problems

UR - http://www.scopus.com/inward/record.url?scp=84893515069&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2013.67

DO - 10.1109/FOCS.2013.67

M3 - Conference contribution

AN - SCOPUS:84893515069

SN - 9780769551357

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 568

EP - 577

BT - Proceedings - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013

T2 - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013

Y2 - 27 October 2013 through 29 October 2013

ER -