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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

Volume

LIPIcs, Volume 55

43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

ICALP 2016, July 11-15, 2016, Rome, Italy

Editors: Ioannis Chatzigiannakis, Michael Mitzenmacher, Yuval Rabani, and Davide Sangiorgi

Document

DOI: 10.4230/LIPIcs.ITCS.2022.114

Uniform Bounds for Scheduling with Job Size Estimates

Authors: Ziv Scully, Isaac Grosof, and Michael Mitzenmacher

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract

We consider the problem of scheduling to minimize mean response time in M/G/1 queues where only estimated job sizes (processing times) are known to the scheduler, where a job of true size s has estimated size in the interval [β s, α s] for some α ≥ β > 0. We evaluate each scheduling policy by its approximation ratio, which we define to be the ratio between its mean response time and that of Shortest Remaining Processing Time (SRPT), the optimal policy when true sizes are known. Our question: is there a scheduling policy that (a) has approximation ratio near 1 when α and β are near 1, (b) has approximation ratio bounded by some function of α and β even when they are far from 1, and (c) can be implemented without knowledge of α and β? We first show that naively running SRPT using estimated sizes in place of true sizes is not such a policy: its approximation ratio can be arbitrarily large for any fixed β < 1. We then provide a simple variant of SRPT for estimated sizes that satisfies criteria (a), (b), and (c). In particular, we prove its approximation ratio approaches 1 uniformly as α and β approach 1. This is the first result showing this type of convergence for M/G/1 scheduling. We also study the Preemptive Shortest Job First (PSJF) policy, a cousin of SRPT. We show that, unlike SRPT, naively running PSJF using estimated sizes in place of true sizes satisfies criteria (b) and (c), as well as a weaker version of (a).

Cite as

Ziv Scully, Isaac Grosof, and Michael Mitzenmacher. Uniform Bounds for Scheduling with Job Size Estimates. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 114:1-114:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{scully_et_al:LIPIcs.ITCS.2022.114,
  author =	{Scully, Ziv and Grosof, Isaac and Mitzenmacher, Michael},
  title =	{{Uniform Bounds for Scheduling with Job Size Estimates}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{114:1--114:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.114},
  URN =		{urn:nbn:de:0030-drops-157108},
  doi =		{10.4230/LIPIcs.ITCS.2022.114},
  annote =	{Keywords: Scheduling, queueing systems, algorithms with predictions, shortest remaining processing time (SRPT), preemptive shortest job first (PSJF), M/G/1 queue}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2021.25

How to Send a Real Number Using a Single Bit (And Some Shared Randomness)

Authors: Ran Ben Basat, Michael Mitzenmacher, and Shay Vargaftik

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract

We consider the fundamental problem of communicating an estimate of a real number x ∈ [0,1] using a single bit. A sender that knows x chooses a value X ∈ {0,1} to transmit. In turn, a receiver estimates x based on the value of X. The goal is to minimize the cost, defined as the worst-case (over the choice of x) expected squared error. We first overview common biased and unbiased estimation approaches and prove their optimality when no shared randomness is allowed. We then show how a small amount of shared randomness, which can be as low as a single bit, reduces the cost in both cases. Specifically, we derive lower bounds on the cost attainable by any algorithm with unrestricted use of shared randomness and propose optimal and near-optimal solutions that use a small number of shared random bits. Finally, we discuss open problems and future directions.

Cite as

Ran Ben Basat, Michael Mitzenmacher, and Shay Vargaftik. How to Send a Real Number Using a Single Bit (And Some Shared Randomness). In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{benbasat_et_al:LIPIcs.ICALP.2021.25,
  author =	{Ben Basat, Ran and Mitzenmacher, Michael and Vargaftik, Shay},
  title =	{{How to Send a Real Number Using a Single Bit (And Some Shared Randomness)}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.25},
  URN =		{urn:nbn:de:0030-drops-140942},
  doi =		{10.4230/LIPIcs.ICALP.2021.25},
  annote =	{Keywords: Randomized Algorithms, Approximation Algorithms, Shared Randomness, Distributed Protocols, Estimation, Subtractive Dithering}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2020.14

Scheduling with Predictions and the Price of Misprediction

Authors: Michael Mitzenmacher

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract

In many traditional job scheduling settings, it is assumed that one knows the time it will take for a job to complete service. In such cases, strategies such as shortest job first can be used to improve performance in terms of measures such as the average time a job waits in the system. We consider the setting where the service time is not known, but is predicted by for example a machine learning algorithm. Our main result is the derivation, under natural assumptions, of formulae for the performance of several strategies for queueing systems that use predictions for service times in order to schedule jobs. As part of our analysis, we suggest the framework of the "price of misprediction," which offers a measure of the cost of using predicted information.

Cite as

Michael Mitzenmacher. Scheduling with Predictions and the Price of Misprediction. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{mitzenmacher:LIPIcs.ITCS.2020.14,
  author =	{Mitzenmacher, Michael},
  title =	{{Scheduling with Predictions and the Price of Misprediction}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.14},
  URN =		{urn:nbn:de:0030-drops-116996},
  doi =		{10.4230/LIPIcs.ITCS.2020.14},
  annote =	{Keywords: Queues, shortest remaining processing time, algorithms with predictions, scheduling}
}

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.

Cite as

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.

Cite as

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].

Cite as

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.

Cite as

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}
}

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