Projects per year
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.
|Title of host publication||Computing and Combinatorics - 26th International Conference, COCOON 2020, Proceedings|
|Editors||Donghyun Kim, R.N. Uma, Zhipeng Cai, Dong Hoon Lee|
|Number of pages||13|
|Publication status||Published - 1 Jan 2020|
|MoE publication type||A4 Article in a conference publication|
|Event|| International Computing and Combinatorics Conference - Atlanta, United States|
Duration: 29 Aug 2020 → 31 Aug 2020
Conference number: 26
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||International Computing and Combinatorics Conference|
|Period||29/08/2020 → 31/08/2020|
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ALGOCom: Novel Algorithmic Techniques through the Lens of Combinatorics
Chalermsook, P., Jindal, G., Franck, M., Spoerhase, J., Yingchareonthawornchai, S., Gadekar, A., Orgo, L., Jiamjitrak, W. & Khodamoradi, K.
01/02/2018 → 31/01/2024
Project: EU: ERC grants