3 Search Results for "Cohen, Avi"

Document
DOI: 10.4230/LIPIcs.MFCS.2021.32
Budgeted Dominating Sets in Uncertain Graphs

Authors: Keerti Choudhary, Avi Cohen, N. S. Narayanaswamy, David Peleg, and R. Vijayaragunathan

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

Abstract
We study the Budgeted Dominating Set (BDS) problem on uncertain graphs, namely, graphs with a probability distribution p associated with the edges, such that an edge e exists in the graph with probability p(e). The input to the problem consists of a vertex-weighted uncertain graph 𝒢 = (V, E, p, ω) and an integer budget (or solution size) k, and the objective is to compute a vertex set S of size k that maximizes the expected total domination (or total weight) of vertices in the closed neighborhood of S. We refer to the problem as the Probabilistic Budgeted Dominating Set (PBDS) problem. In this article, we present the following results on the complexity of the PBDS problem. 1) We show that the PBDS problem is NP-complete even when restricted to uncertain trees of diameter at most four. This is in sharp contrast with the well-known fact that the BDS problem is solvable in polynomial time in trees. We further show that PBDS is 𝖶[1]-hard for the budget parameter k, and under the Exponential time hypothesis it cannot be solved in n^o(k) time. 2) We show that if one is willing to settle for (1-ε) approximation, then there exists a PTAS for PBDS on trees. Moreover, for the scenario of uniform edge-probabilities, the problem can be solved optimally in polynomial time. 3) We consider the parameterized complexity of the PBDS problem, and show that Uni-PBDS (where all edge probabilities are identical) is 𝖶[1]-hard for the parameter pathwidth. On the other hand, we show that it is FPT in the combined parameters of the budget k and the treewidth. 4) Finally, we extend some of our parameterized results to planar and apex-minor-free graphs. Our first hardness proof (Thm. 1) makes use of the new problem of k-Subset Σ-Π Maximization (k-SPM), which we believe is of independent interest. We prove its NP-hardness by a reduction from the well-known k-SUM problem, presenting a close relationship between the two problems.
Cite as

Keerti Choudhary, Avi Cohen, N. S. Narayanaswamy, David Peleg, and R. Vijayaragunathan. Budgeted Dominating Sets in Uncertain Graphs. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{choudhary_et_al:LIPIcs.MFCS.2021.32,
  author =	{Choudhary, Keerti and Cohen, Avi and Narayanaswamy, N. S. and Peleg, David and Vijayaragunathan, R.},
  title =	{{Budgeted Dominating Sets in Uncertain Graphs}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{32:1--32:22},
  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.2021.32},
  URN =		{urn:nbn:de:0030-drops-144723},
  doi =		{10.4230/LIPIcs.MFCS.2021.32},
  annote =	{Keywords: Uncertain graphs, Dominating set, NP-hard, PTAS, treewidth, planar graph}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.10
Minimum Neighboring Degree Realization in Graphs and Trees

Authors: Amotz Bar-Noy, Keerti Choudhary, Avi Cohen, David Peleg, and Dror Rawitz

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
We study a graph realization problem that pertains to degrees in vertex neighborhoods. The classical problem of degree sequence realizability asks whether or not a given sequence of n positive integers is equal to the degree sequence of some n-vertex undirected simple graph. While the realizability problem of degree sequences has been well studied for different classes of graphs, there has been relatively little work concerning the realizability of other types of information profiles, such as the vertex neighborhood profiles. In this paper we introduce and explore the minimum degrees in vertex neighborhood profile as it is one of the most natural extensions of the classical degree profile to vertex neighboring degree profiles. Given a graph G = (V,E), the min-degree of a vertex v ∈ V, namely MinND(v), is given by min{deg(w) ∣ w ∈ N[v]}. Our input is a sequence σ = (d_𝓁^{n_𝓁}, ⋯ , d₁^{n₁}), where d_{i+1} > d_i and each n_i is a positive integer. We provide some necessary and sufficient conditions for σ to be realizable. Furthermore, under the restriction that the realization is acyclic, i.e., a tree or a forest, we provide a full characterization of realizable sequences, along with a corresponding constructive algorithm. We believe our results are a crucial step towards understanding extremal neighborhood degree relations in graphs.
Cite as

Amotz Bar-Noy, Keerti Choudhary, Avi Cohen, David Peleg, and Dror Rawitz. Minimum Neighboring Degree Realization in Graphs and Trees. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{barnoy_et_al:LIPIcs.ESA.2020.10,
  author =	{Bar-Noy, Amotz and Choudhary, Keerti and Cohen, Avi and Peleg, David and Rawitz, Dror},
  title =	{{Minimum Neighboring Degree Realization in Graphs and Trees}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.10},
  URN =		{urn:nbn:de:0030-drops-128765},
  doi =		{10.4230/LIPIcs.ESA.2020.10},
  annote =	{Keywords: Graph realization, neighborhood profile, graph algorithms, degree sequences}
}
Document
DOI: 10.4230/LIPIcs.CCC.2019.9
Typically-Correct Derandomization for Small Time and Space

Authors: William M. Hoza

Published in: LIPIcs, Volume 137, 34th Computational Complexity Conference (CCC 2019)

Abstract
Suppose a language L can be decided by a bounded-error randomized algorithm that runs in space S and time n * poly(S). We give a randomized algorithm for L that still runs in space O(S) and time n * poly(S) that uses only O(S) random bits; our algorithm has a low failure probability on all but a negligible fraction of inputs of each length. As an immediate corollary, there is a deterministic algorithm for L that runs in space O(S) and succeeds on all but a negligible fraction of inputs of each length. We also give several other complexity-theoretic applications of our technique.
Cite as

William M. Hoza. Typically-Correct Derandomization for Small Time and Space. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 9:1-9:39, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{hoza:LIPIcs.CCC.2019.9,
  author =	{Hoza, William M.},
  title =	{{Typically-Correct Derandomization for Small Time and Space}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{9:1--9:39},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Shpilka, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2019.9},
  URN =		{urn:nbn:de:0030-drops-108317},
  doi =		{10.4230/LIPIcs.CCC.2019.9},
  annote =	{Keywords: Derandomization, pseudorandomness, space complexity}
}
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