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DOI: 10.4230/LIPIcs.ESA.2022.17
Simple Dynamic Spanners with Near-Optimal Recourse Against an Adaptive Adversary

Authors: Sayan Bhattacharya, Thatchaphol Saranurak, and Pattara Sukprasert

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
Designing dynamic algorithms against an adaptive adversary whose performance match the ones assuming an oblivious adversary is a major research program in the field of dynamic graph algorithms. One of the prominent examples whose oblivious-vs-adaptive gap remains maximally large is the fully dynamic spanner problem; there exist algorithms assuming an oblivious adversary with near-optimal size-stretch trade-off using only polylog(n) update time [Baswana, Khurana, and Sarkar TALG'12; Forster and Goranci STOC'19; Bernstein, Forster, and Henzinger SODA'20], while against an adaptive adversary, even when we allow infinite time and only count recourse (i.e. the number of edge changes per update in the maintained spanner), all previous algorithms with stretch at most log⁵(n) require at least Ω(n) amortized recourse [Ausiello, Franciosa, and Italiano ESA'05]. In this paper, we completely close this gap with respect to recourse by showing algorithms against an adaptive adversary with near-optimal size-stretch trade-off and recourse. More precisely, for any k ≥ 1, our algorithm maintains a (2k-1)-spanner of size O(n^{1+1/k}log n) with O(log n) amortized recourse, which is optimal in all parameters up to a O(log n) factor. As a step toward algorithms with small update time (not just recourse), we show another algorithm that maintains a 3-spanner of size Õ(n^{1.5}) with polylog(n) amortized recourse and simultaneously Õ(√n) worst-case update time.
Cite as

Sayan Bhattacharya, Thatchaphol Saranurak, and Pattara Sukprasert. Simple Dynamic Spanners with Near-Optimal Recourse Against an Adaptive Adversary. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 17:1-17:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bhattacharya_et_al:LIPIcs.ESA.2022.17,
  author =	{Bhattacharya, Sayan and Saranurak, Thatchaphol and Sukprasert, Pattara},
  title =	{{Simple Dynamic Spanners with Near-Optimal Recourse Against an Adaptive Adversary}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{17:1--17:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.17},
  URN =		{urn:nbn:de:0030-drops-169555},
  doi =		{10.4230/LIPIcs.ESA.2022.17},
  annote =	{Keywords: Algorithms, Dynamic Algorithms, Spanners, Recourse}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.37
Approximating k-Edge-Connected Spanning Subgraphs via a Near-Linear Time LP Solver

Authors: Parinya Chalermsook, Chien-Chung Huang, Danupon Nanongkai, Thatchaphol Saranurak, Pattara Sukprasert, and Sorrachai Yingchareonthawornchai

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
In the k-edge-connected spanning subgraph (kECSS) problem, our goal is to compute a minimum-cost sub-network that is resilient against up to k link failures: Given an n-node m-edge graph with a cost function on the edges, our goal is to compute a minimum-cost k-edge-connected spanning subgraph. This NP-hard problem generalizes the minimum spanning tree problem and is the "uniform case" of a much broader class of survival network design problems (SNDP). A factor of two has remained the best approximation ratio for polynomial-time algorithms for the whole class of SNDP, even for a special case of 2ECSS. The fastest 2-approximation algorithm is however rather slow, taking O(mn k) time [Khuller, Vishkin, STOC'92]. A faster time complexity of O(n²) can be obtained, but with a higher approximation guarantee of (2k-1) [Gabow, Goemans, Williamson, IPCO'93]. Our main contribution is an algorithm that (1+ε)-approximates the optimal fractional solution in Õ(m/ε²) time (independent of k), which can be turned into a (2+ε) approximation algorithm that runs in time Õ(m/(ε²) + {k²n^{1.5}}/ε²) for (integral) kECSS; this improves the running time of the aforementioned results while keeping the approximation ratio arbitrarily close to a factor of two.
Cite as

Parinya Chalermsook, Chien-Chung Huang, Danupon Nanongkai, Thatchaphol Saranurak, Pattara Sukprasert, and Sorrachai Yingchareonthawornchai. Approximating k-Edge-Connected Spanning Subgraphs via a Near-Linear Time LP Solver. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 37:1-37:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chalermsook_et_al:LIPIcs.ICALP.2022.37,
  author =	{Chalermsook, Parinya and Huang, Chien-Chung and Nanongkai, Danupon and Saranurak, Thatchaphol and Sukprasert, Pattara and Yingchareonthawornchai, Sorrachai},
  title =	{{Approximating k-Edge-Connected Spanning Subgraphs via a Near-Linear Time LP Solver}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{37:1--37:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.37},
  URN =		{urn:nbn:de:0030-drops-163785},
  doi =		{10.4230/LIPIcs.ICALP.2022.37},
  annote =	{Keywords: Approximation Algorithms, Data Structures}
}
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