26 Search Results for "Fineman, Jeremy T."

Volume

OASIcs, Volume 69

2nd Symposium on Simplicity in Algorithms (SOSA 2019)

SOSA 2019, January 8-9, 2019, San Diego, CA, USA

Editors: Jeremy T. Fineman and Michael Mitzenmacher

Document
DOI: 10.4230/LIPIcs.ISAAC.2022.36
Nested Active-Time Scheduling

Authors: Nairen Cao, Jeremy T. Fineman, Shi Li, Julián Mestre, Katina Russell, and Seeun William Umboh

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
The active-time scheduling problem considers the problem of scheduling preemptible jobs with windows (release times and deadlines) on a parallel machine that can schedule up to g jobs during each timestep. The goal in the active-time problem is to minimize the number of active steps, i.e., timesteps in which at least one job is scheduled. In this way, the active time models parallel scheduling when there is a fixed cost for turning the machine on at each discrete step. This paper presents a 9/5-approximation algorithm for a special case of the active-time scheduling problem in which job windows are laminar (nested). This result improves on the previous best 2-approximation for the general case.
Cite as

Nairen Cao, Jeremy T. Fineman, Shi Li, Julián Mestre, Katina Russell, and Seeun William Umboh. Nested Active-Time Scheduling. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{cao_et_al:LIPIcs.ISAAC.2022.36,
  author =	{Cao, Nairen and Fineman, Jeremy T. and Li, Shi and Mestre, Juli\'{a}n and Russell, Katina and Umboh, Seeun William},
  title =	{{Nested Active-Time Scheduling}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{36:1--36:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.36},
  URN =		{urn:nbn:de:0030-drops-173214},
  doi =		{10.4230/LIPIcs.ISAAC.2022.36},
  annote =	{Keywords: Scheduling algorithms, Active time, Approximation algorithm}
}
Document
Complete Volume
DOI: 10.4230/OASIcs.SOSA.2019
OASIcs, Volume 69, SOSA'19, Complete Volume

Authors: Jeremy T. Fineman and Michael Mitzenmacher

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
OASIcs, Volume 69, SOSA'19, Complete Volume
Cite as

2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Proceedings{fineman_et_al:OASIcs.SOSA.2019,
  title =	{{OASIcs, Volume 69, SOSA'19, Complete Volume}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019},
  URN =		{urn:nbn:de:0030-drops-101683},
  doi =		{10.4230/OASIcs.SOSA.2019},
  annote =	{Keywords: Theory of computation, Design and analysis of algorithms}
}
Document
Front Matter
DOI: 10.4230/OASIcs.SOSA.2019.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Jeremy T. Fineman and Michael Mitzenmacher

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{fineman_et_al:OASIcs.SOSA.2019.0,
  author =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{0:i--0:x},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.0},
  URN =		{urn:nbn:de:0030-drops-100263},
  doi =		{10.4230/OASIcs.SOSA.2019.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/OASIcs.SOSA.2019.1
Isotonic Regression by Dynamic Programming

Authors: Günter Rote

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
For a given sequence of numbers, we want to find a monotonically increasing sequence of the same length that best approximates it in the sense of minimizing the weighted sum of absolute values of the differences. A conceptually easy dynamic programming approach leads to an algorithm with running time O(n log n). While other algorithms with the same running time are known, our algorithm is very simple. The only auxiliary data structure that it requires is a priority queue. The approach extends to other error measures.
Cite as

Günter Rote. Isotonic Regression by Dynamic Programming. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{rote:OASIcs.SOSA.2019.1,
  author =	{Rote, G\"{u}nter},
  title =	{{Isotonic Regression by Dynamic Programming}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{1:1--1:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.1},
  URN =		{urn:nbn:de:0030-drops-100274},
  doi =		{10.4230/OASIcs.SOSA.2019.1},
  annote =	{Keywords: Convex functions, dynamic programming, convex hull, isotonic regression}
}
Document
DOI: 10.4230/OASIcs.SOSA.2019.2
An Illuminating Algorithm for the Light Bulb Problem

Authors: Josh Alman

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
The Light Bulb Problem is one of the most basic problems in data analysis. One is given as input n vectors in {-1,1}^d, which are all independently and uniformly random, except for a planted pair of vectors with inner product at least rho * d for some constant rho > 0. The task is to find the planted pair. The most straightforward algorithm leads to a runtime of Omega(n^2). Algorithms based on techniques like Locality-Sensitive Hashing achieve runtimes of n^{2 - O(rho)}; as rho gets small, these approach quadratic. Building on prior work, we give a new algorithm for this problem which runs in time O(n^{1.582} + nd), regardless of how small rho is. This matches the best known runtime due to Karppa et al. Our algorithm combines techniques from previous work on the Light Bulb Problem with the so-called `polynomial method in algorithm design,' and has a simpler analysis than previous work. Our algorithm is also easily derandomized, leading to a deterministic algorithm for the Light Bulb Problem with the same runtime of O(n^{1.582} + nd), improving previous results.
Cite as

Josh Alman. An Illuminating Algorithm for the Light Bulb Problem. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 2:1-2:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{alman:OASIcs.SOSA.2019.2,
  author =	{Alman, Josh},
  title =	{{An Illuminating Algorithm for the Light Bulb Problem}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{2:1--2:11},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.2},
  URN =		{urn:nbn:de:0030-drops-100289},
  doi =		{10.4230/OASIcs.SOSA.2019.2},
  annote =	{Keywords: Light Bulb Problem, Polynomial Method, Finding Correlations}
}
Document
DOI: 10.4230/OASIcs.SOSA.2019.3
Simple Concurrent Labeling Algorithms for Connected Components

Authors: Sixue Liu and Robert E. Tarjan

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
We present new concurrent labeling algorithms for finding connected components, and we study their theoretical efficiency. Even though many such algorithms have been proposed and many experiments with them have been done, our algorithms are simpler. We obtain an O(lg n) step bound for two of our algorithms using a novel multi-round analysis. We conjecture that our other algorithms also take O(lg n) steps but are only able to prove an O(lg^2 n) bound. We also point out some gaps in previous analyses of similar algorithms. Our results show that even a basic problem like connected components still has secrets to reveal.
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Sixue Liu and Robert E. Tarjan. Simple Concurrent Labeling Algorithms for Connected Components. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{liu_et_al:OASIcs.SOSA.2019.3,
  author =	{Liu, Sixue and Tarjan, Robert E.},
  title =	{{Simple Concurrent Labeling Algorithms for Connected Components}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{3:1--3:20},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.3},
  URN =		{urn:nbn:de:0030-drops-100292},
  doi =		{10.4230/OASIcs.SOSA.2019.3},
  annote =	{Keywords: Connected Components, Concurrent Algorithms}
}
Document
DOI: 10.4230/OASIcs.SOSA.2019.4
A Framework for Searching in Graphs in the Presence of Errors

Authors: Dariusz Dereniowski, Stefan Tiegel, Przemyslaw Uznanski, and Daniel Wolleb-Graf

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
We consider a problem of searching for an unknown target vertex t in a (possibly edge-weighted) graph. Each vertex-query points to a vertex v and the response either admits that v is the target or provides any neighbor s of v that lies on a shortest path from v to t. This model has been introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide algorithms for the error-less case and for the independent noise model (where each query independently receives an erroneous answer with known probability p<1/2 and a correct one with probability 1-p). We study this problem both with adversarial errors and independent noise models. First, we show an algorithm that needs at most (log_2 n)/(1 - H(r)) queries in case of adversarial errors, where the adversary is bounded with its rate of errors by a known constant r<1/2. Our algorithm is in fact a simplification of previous work, and our refinement lies in invoking an amortization argument. We then show that our algorithm coupled with a Chernoff bound argument leads to a simpler algorithm for the independent noise model and has a query complexity that is both simpler and asymptotically better than the one of Emamjomeh-Zadeh et al. [STOC 2016]. Our approach has a wide range of applications. First, it improves and simplifies the Robust Interactive Learning framework proposed by Emamjomeh-Zadeh and Kempe [NIPS 2017]. Secondly, performing analogous analysis for edge-queries (where a query to an edge e returns its endpoint that is closer to the target) we actually recover (as a special case) a noisy binary search algorithm that is asymptotically optimal, matching the complexity of Feige et al. [SIAM J. Comput. 1994]. Thirdly, we improve and simplify upon an algorithm for searching of unbounded domains due to Aslam and Dhagat [STOC 1991].
Cite as

Dariusz Dereniowski, Stefan Tiegel, Przemyslaw Uznanski, and Daniel Wolleb-Graf. A Framework for Searching in Graphs in the Presence of Errors. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{dereniowski_et_al:OASIcs.SOSA.2019.4,
  author =	{Dereniowski, Dariusz and Tiegel, Stefan and Uznanski, Przemyslaw and Wolleb-Graf, Daniel},
  title =	{{A Framework for Searching in Graphs in the Presence of Errors}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{4:1--4:17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.4},
  URN =		{urn:nbn:de:0030-drops-100305},
  doi =		{10.4230/OASIcs.SOSA.2019.4},
  annote =	{Keywords: graph algorithms, noisy binary search, query complexity, reliability}
}
Document
DOI: 10.4230/OASIcs.SOSA.2019.5
Selection from Heaps, Row-Sorted Matrices, and X+Y Using Soft Heaps

Authors: Haim Kaplan, László Kozma, Or Zamir, and Uri Zwick

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
We use soft heaps to obtain simpler optimal algorithms for selecting the k-th smallest item, and the set of k smallest items, from a heap-ordered tree, from a collection of sorted lists, and from X+Y, where X and Y are two unsorted sets. Our results match, and in some ways extend and improve, classical results of Frederickson (1993) and Frederickson and Johnson (1982). In particular, for selecting the k-th smallest item, or the set of k smallest items, from a collection of m sorted lists we obtain a new optimal "output-sensitive" algorithm that performs only O(m + sum_{i=1}^m log(k_i+1)) comparisons, where k_i is the number of items of the i-th list that belong to the overall set of k smallest items.
Cite as

Haim Kaplan, László Kozma, Or Zamir, and Uri Zwick. Selection from Heaps, Row-Sorted Matrices, and X+Y Using Soft Heaps. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kaplan_et_al:OASIcs.SOSA.2019.5,
  author =	{Kaplan, Haim and Kozma, L\'{a}szl\'{o} and Zamir, Or and Zwick, Uri},
  title =	{{Selection from Heaps, Row-Sorted Matrices, and X+Y Using Soft Heaps}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{5:1--5:21},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.5},
  URN =		{urn:nbn:de:0030-drops-100315},
  doi =		{10.4230/OASIcs.SOSA.2019.5},
  annote =	{Keywords: selection, soft heap}
}
Document
DOI: 10.4230/OASIcs.SOSA.2019.6
Approximating Optimal Transport With Linear Programs

Authors: Kent Quanrud

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation algorithms for optimal transport.
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Kent Quanrud. Approximating Optimal Transport With Linear Programs. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 6:1-6:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{quanrud:OASIcs.SOSA.2019.6,
  author =	{Quanrud, Kent},
  title =	{{Approximating Optimal Transport With Linear Programs}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{6:1--6:9},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.6},
  URN =		{urn:nbn:de:0030-drops-100321},
  doi =		{10.4230/OASIcs.SOSA.2019.6},
  annote =	{Keywords: optimal transport, fast approximations, linear programming}
}
Document
DOI: 10.4230/OASIcs.SOSA.2019.7
LP Relaxation and Tree Packing for Minimum k-cuts

Authors: Chandra Chekuri, Kent Quanrud, and Chao Xu

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
Karger used spanning tree packings [Karger, 2000] to derive a near linear-time randomized algorithm for the global minimum cut problem as well as a bound on the number of approximate minimum cuts. This is a different approach from his well-known random contraction algorithm [Karger, 1995; Karger and Stein, 1996]. Thorup developed a fast deterministic algorithm for the minimum k-cut problem via greedy recursive tree packings [Thorup, 2008]. In this paper we revisit properties of an LP relaxation for k-cut proposed by Naor and Rabani [Naor and Rabani, 2001], and analyzed in [Chekuri et al., 2006]. We show that the dual of the LP yields a tree packing, that when combined with an upper bound on the integrality gap for the LP, easily and transparently extends Karger's analysis for mincut to the k-cut problem. In addition to the simplicity of the algorithm and its analysis, this allows us to improve the running time of Thorup's algorithm by a factor of n. We also improve the bound on the number of alpha-approximate k-cuts. Second, we give a simple proof that the integrality gap of the LP is 2(1-1/n). Third, we show that an optimum solution to the LP relaxation, for all values of k, is fully determined by the principal sequence of partitions of the input graph. This allows us to relate the LP relaxation to the Lagrangean relaxation approach of Barahona [Barahona, 2000] and Ravi and Sinha [Ravi and Sinha, 2008]; it also shows that the idealized recursive tree packing considered by Thorup gives an optimum dual solution to the LP. This work arose from an effort to understand and simplify the results of Thorup [Thorup, 2008].
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Chandra Chekuri, Kent Quanrud, and Chao Xu. LP Relaxation and Tree Packing for Minimum k-cuts. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chekuri_et_al:OASIcs.SOSA.2019.7,
  author =	{Chekuri, Chandra and Quanrud, Kent and Xu, Chao},
  title =	{{LP Relaxation and Tree Packing for Minimum k-cuts}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{7:1--7:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.7},
  URN =		{urn:nbn:de:0030-drops-100335},
  doi =		{10.4230/OASIcs.SOSA.2019.7},
  annote =	{Keywords: k-cut, LP relaxation, tree packing}
}
Document
DOI: 10.4230/OASIcs.SOSA.2019.8
On Primal-Dual Circle Representations

Authors: Stefan Felsner and Günter Rote

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
The Koebe-Andreev-Thurston Circle Packing Theorem states that every triangulated planar graph has a contact representation by circles. The theorem has been generalized in various ways. The most prominent generalization assures the existence of a primal-dual circle representation for every 3-connected planar graph. We present a simple and elegant elementary proof of this result.
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Stefan Felsner and Günter Rote. On Primal-Dual Circle Representations. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{felsner_et_al:OASIcs.SOSA.2019.8,
  author =	{Felsner, Stefan and Rote, G\"{u}nter},
  title =	{{On Primal-Dual Circle Representations}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{8:1--8:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.8},
  URN =		{urn:nbn:de:0030-drops-100349},
  doi =		{10.4230/OASIcs.SOSA.2019.8},
  annote =	{Keywords: Disk packing, planar graphs, contact representation}
}
Document
DOI: 10.4230/OASIcs.SOSA.2019.9
Asymmetric Convex Intersection Testing

Authors: Luis Barba and Wolfgang Mulzer

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
We consider asymmetric convex intersection testing (ACIT). Let P subset R^d be a set of n points and H a set of n halfspaces in d dimensions. We denote by {ch(P)} the polytope obtained by taking the convex hull of P, and by {fh(H)} the polytope obtained by taking the intersection of the halfspaces in H. Our goal is to decide whether the intersection of H and the convex hull of P are disjoint. Even though ACIT is a natural variant of classic LP-type problems that have been studied at length in the literature, and despite its applications in the analysis of high-dimensional data sets, it appears that the problem has not been studied before. We discuss how known approaches can be used to attack the ACIT problem, and we provide a very simple strategy that leads to a deterministic algorithm, linear on n and m, whose running time depends reasonably on the dimension d.
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Luis Barba and Wolfgang Mulzer. Asymmetric Convex Intersection Testing. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{barba_et_al:OASIcs.SOSA.2019.9,
  author =	{Barba, Luis and Mulzer, Wolfgang},
  title =	{{Asymmetric Convex Intersection Testing}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{9:1--9:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.9},
  URN =		{urn:nbn:de:0030-drops-100358},
  doi =		{10.4230/OASIcs.SOSA.2019.9},
  annote =	{Keywords: polytope intersection, LP-type problem, randomized algorithm}
}
Document
DOI: 10.4230/OASIcs.SOSA.2019.10
Relaxed Voronoi: A Simple Framework for Terminal-Clustering Problems

Authors: Arnold Filtser, Robert Krauthgamer, and Ohad Trabelsi

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
We reprove three known algorithmic bounds for terminal-clustering problems, using a single framework that leads to simpler proofs. In this genre of problems, the input is a metric space (X,d) (possibly arising from a graph) and a subset of terminals K subset X, and the goal is to partition the points X such that each part, called a cluster, contains exactly one terminal (possibly with connectivity requirements) so as to minimize some objective. The three bounds we reprove are for Steiner Point Removal on trees [Gupta, SODA 2001], for Metric 0-Extension in bounded doubling dimension [Lee and Naor, unpublished 2003], and for Connected Metric 0-Extension [Englert et al., SICOMP 2014]. A natural approach is to cluster each point with its closest terminal, which would partition X into so-called Voronoi cells, but this approach can fail miserably due to its stringent cluster boundaries. A now-standard fix, which we call the Relaxed-Voronoi framework, is to use enlarged Voronoi cells, but to obtain disjoint clusters, the cells are computed greedily according to some order. This method, first proposed by Calinescu, Karloff and Rabani [SICOMP 2004], was employed successfully to provide state-of-the-art results for terminal-clustering problems on general metrics. However, for restricted families of metrics, e.g., trees and doubling metrics, only more complicated, ad-hoc algorithms are known. Our main contribution is to demonstrate that the Relaxed-Voronoi algorithm is applicable to restricted metrics, and actually leads to relatively simple algorithms and analyses.
Cite as

Arnold Filtser, Robert Krauthgamer, and Ohad Trabelsi. Relaxed Voronoi: A Simple Framework for Terminal-Clustering Problems. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{filtser_et_al:OASIcs.SOSA.2019.10,
  author =	{Filtser, Arnold and Krauthgamer, Robert and Trabelsi, Ohad},
  title =	{{Relaxed Voronoi: A Simple Framework for Terminal-Clustering Problems}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{10:1--10:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.10},
  URN =		{urn:nbn:de:0030-drops-100369},
  doi =		{10.4230/OASIcs.SOSA.2019.10},
  annote =	{Keywords: Clustering, Steiner point removal, Zero extension, Doubling dimension, Relaxed voronoi}
}
Document
DOI: 10.4230/OASIcs.SOSA.2019.11
Towards a Unified Theory of Sparsification for Matching Problems

Authors: Sepehr Assadi and Aaron Bernstein

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
In this paper, we present a construction of a "matching sparsifier", that is, a sparse subgraph of the given graph that preserves large matchings approximately and is robust to modifications of the graph. We use this matching sparsifier to obtain several new algorithmic results for the maximum matching problem: - An almost (3/2)-approximation one-way communication protocol for the maximum matching problem, significantly simplifying the (3/2)-approximation protocol of Goel, Kapralov, and Khanna (SODA 2012) and extending it from bipartite graphs to general graphs. - An almost (3/2)-approximation algorithm for the stochastic matching problem, improving upon and significantly simplifying the previous 1.999-approximation algorithm of Assadi, Khanna, and Li (EC 2017). - An almost (3/2)-approximation algorithm for the fault-tolerant matching problem, which, to our knowledge, is the first non-trivial algorithm for this problem. Our matching sparsifier is obtained by proving new properties of the edge-degree constrained subgraph (EDCS) of Bernstein and Stein (ICALP 2015; SODA 2016) - designed in the context of maintaining matchings in dynamic graphs - that identifies EDCS as an excellent choice for a matching sparsifier. This leads to surprisingly simple and non-technical proofs of the above results in a unified way. Along the way, we also provide a much simpler proof of the fact that an EDCS is guaranteed to contain a large matching, which may be of independent interest.
Cite as

Sepehr Assadi and Aaron Bernstein. Towards a Unified Theory of Sparsification for Matching Problems. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{assadi_et_al:OASIcs.SOSA.2019.11,
  author =	{Assadi, Sepehr and Bernstein, Aaron},
  title =	{{Towards a Unified Theory of Sparsification for Matching Problems}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{11:1--11:20},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.11},
  URN =		{urn:nbn:de:0030-drops-100370},
  doi =		{10.4230/OASIcs.SOSA.2019.11},
  annote =	{Keywords: Maximum matching, matching sparsifiers, one-way communication complexity, stochastic matching, fault-tolerant matching}
}
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