3 Search Results for "Robertson, Matthew"

Document
DOI: 10.4230/LIPIcs.ESA.2025.7
Graph Modification of Bounded Size to Minor-Closed Classes as Fast as Vertex Deletion

Authors: Laure Morelle, Ignasi Sau, and Dimitrios M. Thilikos

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A replacement action is a function ℒ that maps each graph H to a collection of graphs of size at most |V(H)|. Given a graph class ℋ, we consider a general family of graph modification problems, called ℒ-Replacement to ℋ, where the input is a graph G and the question is whether it is possible to replace some induced subgraph H₁ of G on at most k vertices by a graph H₂ in ℒ(H₁) so that the resulting graph belongs to ℋ. ℒ-Replacement to ℋ can simulate many graph modification problems including vertex deletion, edge deletion/addition/edition/contraction, vertex identification, subgraph complementation, independent set deletion, (induced) matching deletion/contraction, etc. We present two algorithms. The first one solves ℒ-Replacement to ℋ in time 2^poly(k) ⋅ |V(G)|² for every minor-closed graph class ℋ, where poly is a polynomial whose degree depends on ℋ, under a mild technical condition on ℒ. This generalizes the results of Morelle, Sau, Stamoulis, and Thilikos [ICALP 2020, ICALP 2023] for the particular case of Vertex Deletion to ℋ within the same running time. Our second algorithm is an improvement of the first one when ℋ is the class of graphs embeddable in a surface of Euler genus at most g and runs in time 2^𝒪(k⁹) ⋅ |V(G)|², where the 𝒪(⋅) notation depends on g. To the best of our knowledge, these are the first parameterized algorithms with a reasonable parametric dependence for such a general family of graph modification problems to minor-closed classes.
Cite as

Laure Morelle, Ignasi Sau, and Dimitrios M. Thilikos. Graph Modification of Bounded Size to Minor-Closed Classes as Fast as Vertex Deletion. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{morelle_et_al:LIPIcs.ESA.2025.7,
  author =	{Morelle, Laure and Sau, Ignasi and Thilikos, Dimitrios M.},
  title =	{{Graph Modification of Bounded Size to Minor-Closed Classes as Fast as Vertex Deletion}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.7},
  URN =		{urn:nbn:de:0030-drops-244751},
  doi =		{10.4230/LIPIcs.ESA.2025.7},
  annote =	{Keywords: Graph modification problems, Parameterized complexity, Graph minors, Flat Wall theorem, Irrelevant vertex technique, Algorithmic meta-theorem, Parametric dependence, Dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.38
Efficient Algorithms for Demand-Aware Networks and a Connection to Virtual Network Embedding

Authors: Aleksander Figiel, Janne H. Korhonen, Neil Olver, and Stefan Schmid

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
Emerging optical switching technologies enable demand-aware datacenter networks, whose topology can be flexibly optimized toward the traffic they serve. This paper revisits the bounded-degree network design problem underlying such demand-aware networks. Namely, given a distribution over communicating node pairs (represented has a demand graph), we want to design a network with bounded maximum degree (called host graph) that minimizes the expected communication distance. We improve the understanding of this problem domain by filling several gaps in prior work. First, we present the first practical algorithm for solving this problem on arbitrary instances without violating the degree bound. Our algorithm is based on novel insights obtained from studying a new Steiner node version of the problem, and we report on an extensive empirical evaluation, using several real-world traffic traces from datacenters, finding that our approach results in improved demand-aware network designs. Second, we shed light on the complexity and hardness of the bounded-degree network design problem by formally establishing its NP-completeness for any degree. We use our techniques to improve prior upper bounds for sparse instances. Finally, we study an intriguing connection between demand-aware network design and the virtual networking embedding problem, and show that the latter cannot be used to approximate the former: there is no universal host graph which can provide a constant approximation for our problem.
Cite as

Aleksander Figiel, Janne H. Korhonen, Neil Olver, and Stefan Schmid. Efficient Algorithms for Demand-Aware Networks and a Connection to Virtual Network Embedding. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 38:1-38:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{figiel_et_al:LIPIcs.OPODIS.2024.38,
  author =	{Figiel, Aleksander and Korhonen, Janne H. and Olver, Neil and Schmid, Stefan},
  title =	{{Efficient Algorithms for Demand-Aware Networks and a Connection to Virtual Network Embedding}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{38:1--38:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.38},
  URN =		{urn:nbn:de:0030-drops-225742},
  doi =		{10.4230/LIPIcs.OPODIS.2024.38},
  annote =	{Keywords: demand-aware networks, algorithms, virtual network embedding}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2016.29
Raising Permutations to Powers in Place

Authors: Hicham El-Zein, J. Ian Munro, and Matthew Robertson

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

Abstract
Given a permutation of n elements, stored as an array, we address the problem of replacing the permutation by its kth power. We aim to perform this operation quickly using o(n) bits of extra storage. To this end, we first present an algorithm for inverting permutations that uses O(lg^2 n) additional bits and runs in O(n lg n) worst case time. This result is then generalized to the situation in which the permutation is to be replaced by its kth power. An algorithm whose worst case running time is O(n lg n) and uses O(lg^2 n + min{k lg n, n^{3/4 + epsilon}}) additional bits is presented.
Cite as

Hicham El-Zein, J. Ian Munro, and Matthew Robertson. Raising Permutations to Powers in Place. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 29:1-29:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{elzein_et_al:LIPIcs.ISAAC.2016.29,
  author =	{El-Zein, Hicham and Munro, J. Ian and Robertson, Matthew},
  title =	{{Raising Permutations to Powers in Place}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{29:1--29:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.29},
  URN =		{urn:nbn:de:0030-drops-67992},
  doi =		{10.4230/LIPIcs.ISAAC.2016.29},
  annote =	{Keywords: Algorithms, Combinatorics, Inplace, Permutations, Powers}
}
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