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DOI: 10.4230/LIPIcs.ESA.2017.64

Clustering in Hypergraphs to Minimize Average Edge Service Time

Authors: Ori Rottenstreich, Haim Kaplan, and Avinatan Hassidim

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract

We study the problem of clustering the vertices of a weighted hypergraph such that on average the vertices of each edge can be covered by a small number of clusters. This problem has many applications such as for designing medical tests, clustering files on disk servers, and placing network services on servers. The edges of the hypergraph model groups of items that are likely to be needed together, and the optimization criteria which we use can be interpreted as the average delay (or cost) to serve the items of a typical edge. We describe and analyze algorithms for this problem for the case in which the clusters have to be disjoint and for the case where clusters can overlap. The analysis is often subtle and reveals interesting structure and invariants that one can utilize.

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Ori Rottenstreich, Haim Kaplan, and Avinatan Hassidim. Clustering in Hypergraphs to Minimize Average Edge Service Time. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 64:1-64:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{rottenstreich_et_al:LIPIcs.ESA.2017.64,
  author =	{Rottenstreich, Ori and Kaplan, Haim and Hassidim, Avinatan},
  title =	{{Clustering in Hypergraphs to Minimize Average Edge Service Time}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{64:1--64:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.64},
  URN =		{urn:nbn:de:0030-drops-78777},
  doi =		{10.4230/LIPIcs.ESA.2017.64},
  annote =	{Keywords: Clustering, average cover time, hypergraphs, set cover}
}

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DOI: 10.4230/LIPIcs.STACS.2010.2450

Quantum Algorithms for Testing Properties of Distributions

Authors: Sergey Bravyi, Aram W. Harrow, and Avinatan Hassidim

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract

Suppose one has access to oracles generating samples from two unknown probability distributions $p$ and $q$ on some $N$-element set. How many samples does one need to test whether the two distributions are close or far from each other in the $L_1$-norm? This and related questions have been extensively studied during the last years in the field of property testing. In the present paper we study quantum algorithms for testing properties of distributions. It is shown that the $L_1$-distance $\|p-q\|_1$ can be estimated with a constant precision using only $O(N^{1/2})$ queries in the quantum settings, whereas classical computers need $\Omega(N^{1-o(1)})$ queries. We also describe quantum algorithms for testing Uniformity and Orthogonality with query complexity $O(N^{1/3})$. The classical query complexity of these problems is known to be $\Omega(N^{1/2})$. A quantum algorithm for testing Uniformity has been recently independently discovered by Chakraborty et al. \cite{CFMW09}.

Cite as

Sergey Bravyi, Aram W. Harrow, and Avinatan Hassidim. Quantum Algorithms for Testing Properties of Distributions. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 131-142, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{bravyi_et_al:LIPIcs.STACS.2010.2450,
  author =	{Bravyi, Sergey and Harrow, Aram W. and Hassidim, Avinatan},
  title =	{{Quantum Algorithms for Testing Properties of Distributions}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{131--142},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2450},
  URN =		{urn:nbn:de:0030-drops-24502},
  doi =		{10.4230/LIPIcs.STACS.2010.2450},
  annote =	{Keywords: Quantum computing, property testing, sampling}
}

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Documents authored by Hassidim, Avinatan

Clustering in Hypergraphs to Minimize Average Edge Service Time

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Quantum Algorithms for Testing Properties of Distributions

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