A Simple Primal-Dual Approximation Algorithm for 2-Edge-Connected Spanning Subgraphs

Stephan Beyer, Markus Chimani, Joachim Spoerhase*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

Our paper is motivated by the search for combinatorial and, in particular, primal-dual approximation algorithms for higher-connectivity survivable network design problems (SND). The best known approximation algorithm for SND is Jain’s powerful but “non-combinatorial” iterative LP-rounding technique, which yields factor 2. In contrast, known combinatorial algorithms are based on multi-phase primal-dual approaches that increase the connectivity in each phase, thereby naturally leading to a factor depending (logarithmically) on the maximum connectivity requirement. Williamson raised the question if there are single-phase primal-dual algorithms for such problems. A single-phase primal-dual algorithm could potentially be key to a primal-dual constant-factor approximation algorithm for SND. Whether such an algorithm exists is an important open problem (Shmoys and Williamson). In this paper, we make a first, small step related to these questions. We show that there is a primal-dual algorithm for the minimum 2-edge-connected spanning subgraph problem (2ECSS) that requires only a single growing phase and that is therefore the first such algorithm for any higher-connectivity problem. The algorithm yields approximation factor 3, which matches the factor of the best known (two-phase) primal-dual approximation algorithms for 2ECSS. Moreover, we believe that our algorithm is more natural and conceptually simpler than the known primal-dual algorithms for 2ECSS. It can be implemented without data structures more sophisticated than binary heaps and graphs, and without graph algorithms beyond depth-first search.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 26th International Conference, COCOON 2020, Proceedings
EditorsDonghyun Kim, R.N. Uma, Zhipeng Cai, Dong Hoon Lee
PublisherSpringer Science and Business Media Deutschland GmbH
Pages347-359
Number of pages13
ISBN (Print)9783030581497
DOIs
Publication statusPublished - 1 Jan 2020
MoE publication typeA4 Article in a conference publication
Event International Computing and Combinatorics Conference - Atlanta, United States
Duration: 29 Aug 202031 Aug 2020
Conference number: 26

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer
Volume12273 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference International Computing and Combinatorics Conference
Abbreviated titleCOCOON
CountryUnited States
CityAtlanta
Period29/08/202031/08/2020

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    Beyer, S., Chimani, M., & Spoerhase, J. (2020). A Simple Primal-Dual Approximation Algorithm for 2-Edge-Connected Spanning Subgraphs. In D. Kim, R. N. Uma, Z. Cai, & D. H. Lee (Eds.), Computing and Combinatorics - 26th International Conference, COCOON 2020, Proceedings (pp. 347-359). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12273 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-58150-3_28