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Documents authored by Harutyunyan, Hovhannes A.

Document
DOI: 10.4230/LIPIcs.ISAAC.2023.38
Temporal Separators with Deadlines

Authors: Hovhannes A. Harutyunyan, Kamran Koupayi, and Denis Pankratov

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
We study temporal analogues of the Unrestricted Vertex Separator problem from the static world. An (s,z)-temporal separator is a set of vertices whose removal disconnects vertex s from vertex z for every time step in a temporal graph. The (s,z)-Temporal Separator problem asks to find the minimum size of an (s,z)-temporal separator for the given temporal graph. The (s,z)-Temporal Separator problem is known to be NP-hard in general, although some special cases (such as bounded treewidth) admit efficient algorithms [Fluschnik et al., 2020]. We introduce a generalization of this problem called the (s,z,t)-Temporal Separator problem, where the goal is to find a smallest subset of vertices whose removal eliminates all temporal paths from s to z which take less than t time steps. Let τ denote the number of time steps over which the temporal graph is defined (we consider discrete time steps). We characterize the set of parameters τ and t when the problem is NP-hard and when it is polynomial time solvable. Then we present a τ-approximation algorithm for the (s,z)-Temporal Separator problem and convert it to a τ²-approximation algorithm for the (s,z,t)-Temporal Separator problem. We also present an inapproximability lower bound of Ω(ln(n) + ln(τ)) for the (s,z,t)-Temporal Separator problem assuming that NP ⊄ DTIME(n^{log log n}). Then we consider three special families of graphs: (1) graphs of branchwidth at most 2, (2) graphs G such that the removal of s and z leaves a tree, and (3) graphs of bounded pathwidth. We present polynomial-time algorithms to find a minimum (s,z,t)-temporal separator for (1) and (2). As for (3), we show a polynomial-time reduction from the Discrete Segment Covering problem with bounded-length segments to the (s,z,t)-Temporal Separator problem where the temporal graph has bounded pathwidth.
Cite as

Hovhannes A. Harutyunyan, Kamran Koupayi, and Denis Pankratov. Temporal Separators with Deadlines. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 38:1-38:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{harutyunyan_et_al:LIPIcs.ISAAC.2023.38,
  author =	{Harutyunyan, Hovhannes A. and Koupayi, Kamran and Pankratov, Denis},
  title =	{{Temporal Separators with Deadlines}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{38:1--38:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.38},
  URN =		{urn:nbn:de:0030-drops-193407},
  doi =		{10.4230/LIPIcs.ISAAC.2023.38},
  annote =	{Keywords: Temporal graphs, dynamic graphs, vertex separator, vertex cut, separating set, deadlines, inapproximability, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.57
Online Domination: The Value of Getting to Know All Your Neighbors

Authors: Hovhannes A. Harutyunyan, Denis Pankratov, and Jesse Racicot

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
We study the dominating set problem in an online setting. An algorithm is required to guarantee competitiveness against an adversary that reveals the input graph one node at a time. When a node is revealed, the algorithm learns about the entire neighborhood of the node (including those nodes that have not yet been revealed). Furthermore, the adversary is required to keep the revealed portion of the graph connected at all times. We present an algorithm that achieves 2-competitiveness on trees. We also present algorithms that achieve 2.5-competitiveness on cactus graphs, (t-1)-competitiveness on K_{1,t}-free graphs, and Θ(√{Δ}) for maximum degree Δ graphs. We show that all of those competitive ratios are tight. Then, we study several more general classes of graphs, such as threshold, bipartite planar, and series-parallel graphs, and show that they do not admit competitive algorithms (i.e., when competitive ratio is independent of the input size). Previously, the dominating set problem was considered in a different input model (often together with the restriction of the input graph being always connected), where a vertex is revealed alongside its restricted neighborhood: those neighbors that are among already revealed vertices. Thus, conceptually, our results quantify the value of knowing the entire neighborhood at the time a vertex is revealed as compared to the restricted neighborhood. For instance, it was known in the restricted neighborhood model that 3-competitiveness is optimal for trees, whereas knowing the neighbors allows us to improve it to 2-competitiveness.
Cite as

Hovhannes A. Harutyunyan, Denis Pankratov, and Jesse Racicot. Online Domination: The Value of Getting to Know All Your Neighbors. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 57:1-57:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{harutyunyan_et_al:LIPIcs.MFCS.2021.57,
  author =	{Harutyunyan, Hovhannes A. and Pankratov, Denis and Racicot, Jesse},
  title =	{{Online Domination: The Value of Getting to Know All Your Neighbors}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{57:1--57:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.57},
  URN =		{urn:nbn:de:0030-drops-144979},
  doi =		{10.4230/LIPIcs.MFCS.2021.57},
  annote =	{Keywords: Dominating set, online algorithms, competitive ratio, trees, cactus graphs, bipartite planar graphs, series-parallel graphs, closed neighborhood}
}
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