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DOI: 10.4230/LIPIcs.ESA.2024.74

Improved Approximations for Flexible Network Design

Authors: Dylan Hyatt-Denesik, Afrouz Jabal-Ameli, and Laura Sanità

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract

Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a given graph are here partitioned into safe and unsafe. The goal is to identify a minimum size subgraph that is 2-edge-connected (resp. 2-vertex-connected), and stay so whenever any of the unsafe elements gets removed. In this paper, we provide improved approximation algorithms for flexible network design problems, considering both edge-connectivity and vertex-connectivity, as well as connectivity values higher than 2. For the vertex-connectivity variant, in particular, our algorithm is the first with approximation factor strictly better than 2.

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Dylan Hyatt-Denesik, Afrouz Jabal-Ameli, and Laura Sanità. Improved Approximations for Flexible Network Design. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 74:1-74:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hyattdenesik_et_al:LIPIcs.ESA.2024.74,
  author =	{Hyatt-Denesik, Dylan and Jabal-Ameli, Afrouz and Sanit\`{a}, Laura},
  title =	{{Improved Approximations for Flexible Network Design}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{74:1--74:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.74},
  URN =		{urn:nbn:de:0030-drops-211456},
  doi =		{10.4230/LIPIcs.ESA.2024.74},
  annote =	{Keywords: Approximation Algorithms, Network Design, Flexible Connectivity}
}

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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2023.79

Finding Almost Tight Witness Trees

Authors: Dylan Hyatt-Denesik, Afrouz Jabal Ameli, and Laura Sanità

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract

This paper addresses a graph optimization problem, called the Witness Tree problem, which seeks a spanning tree of a graph minimizing a certain non-linear objective function. This problem is of interest because it plays a crucial role in the analysis of the best approximation algorithms for two fundamental network design problems: Steiner Tree and Node-Tree Augmentation. We will show how a wiser choice of witness trees leads to an improved approximation for Node-Tree Augmentation, and for Steiner Tree in special classes of graphs.

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Dylan Hyatt-Denesik, Afrouz Jabal Ameli, and Laura Sanità. Finding Almost Tight Witness Trees. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 79:1-79:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hyattdenesik_et_al:LIPIcs.ICALP.2023.79,
  author =	{Hyatt-Denesik, Dylan and Jabal Ameli, Afrouz and Sanit\`{a}, Laura},
  title =	{{Finding Almost Tight Witness Trees}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{79:1--79:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.79},
  URN =		{urn:nbn:de:0030-drops-181314},
  doi =		{10.4230/LIPIcs.ICALP.2023.79},
  annote =	{Keywords: Algorithms, Network Design, Approximation}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2020.11

Approximations for Throughput Maximization

Authors: Dylan Hyatt-Denesik, Mirmahdi Rahgoshay, and Mohammad R. Salavatipour

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract

In this paper we study the classical problem of throughput maximization. In this problem we have a collection J of n jobs, each having a release time r_j, deadline d_j, and processing time p_j. They have to be scheduled non-preemptively on m identical parallel machines. The goal is to find a schedule which maximizes the number of jobs scheduled entirely in their [r_j,d_j] window. This problem has been studied extensively (even for the case of m = 1). Several special cases of the problem remain open. Bar-Noy et al. [STOC1999] presented an algorithm with ratio 1-1/(1+1/m)^m for m machines, which approaches 1-1/e as m increases. For m = 1, Chuzhoy-Ostrovsky-Rabani [FOCS2001] presented an algorithm with approximation with ratio 1-1/e-ε (for any ε > 0). Recently Im-Li-Moseley [IPCO2017] presented an algorithm with ratio 1-1/e+ε₀ for some absolute constant ε₀ > 0 for any fixed m. They also presented an algorithm with ratio 1-O(√(log m/m))-ε for general m which approaches 1 as m grows. The approximability of the problem for m = O(1) remains a major open question. Even for the case of m = 1 and c = O(1) distinct processing times the problem is open (Sgall [ESA2012]). In this paper we study the case of m = O(1) and show that if there are c distinct processing times, i.e. p_j’s come from a set of size c, then there is a randomized (1-ε)-approximation that runs in time O(n^{mc⁷ε^(-6)}log T), where T is the largest deadline. Therefore, for constant m and constant c this yields a PTAS. Our algorithm is based on proving structural properties for a near optimum solution that allows one to use a dynamic programming with pruning.

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Dylan Hyatt-Denesik, Mirmahdi Rahgoshay, and Mohammad R. Salavatipour. Approximations for Throughput Maximization. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{hyattdenesik_et_al:LIPIcs.ISAAC.2020.11,
  author =	{Hyatt-Denesik, Dylan and Rahgoshay, Mirmahdi and Salavatipour, Mohammad R.},
  title =	{{Approximations for Throughput Maximization}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.11},
  URN =		{urn:nbn:de:0030-drops-133555},
  doi =		{10.4230/LIPIcs.ISAAC.2020.11},
  annote =	{Keywords: Scheduling, Approximation Algorithms, Throughput Maximization}
}

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Documents authored by Hyatt-Denesik, Dylan

Improved Approximations for Flexible Network Design

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Finding Almost Tight Witness Trees

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Approximations for Throughput Maximization

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