12 Search Results for "Englert, Matthias"


Document
Approximation Guarantees for Shortest Superstrings: Simpler and Better

Authors: Matthias Englert, Nicolaos Matsakis, and Pavel Veselý

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


Abstract
The Shortest Superstring problem is an NP-hard problem, in which given as input a set of strings, we are looking for a string of minimum length that contains all input strings as substrings. The Greedy Conjecture (Tarhio and Ukkonen, 1988) states that the GREEDY algorithm, which repeatedly merges the two strings of maximum overlap, is 2-approximate. We have recently shown (STOC 2022) that the approximation guarantee of GREEDY is at most (13+√{57})/6 ≈ 3.425. Before that, the best established upper bound for this was 3.5 by Kaplan and Shafrir (IPL 2005), which improved upon the upper bound of 4 by Blum et al. (STOC 1991). To derive our previous result, we established two incomparable upper bounds on the overlap sum of all cycle-closing edges in an optimal cycle cover and utilized lemmas of Blum et al. We improve the more involved one of the two bounds and, at the same time, make its proof more straightforward. This results in an improved approximation guarantee of (√{67}+2)/3 ≈ 3.396 for GREEDY. Additionally, our result implies an algorithm for the Shortest Superstring problem having an approximation guarantee of (√{67}+14)/9 ≈ 2.466, improving slightly upon the previously best guarantee of (√{57}+37)/18 ≈ 2.475 (STOC 2022).

Cite as

Matthias Englert, Nicolaos Matsakis, and Pavel Veselý. Approximation Guarantees for Shortest Superstrings: Simpler and Better. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 29:1-29:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{englert_et_al:LIPIcs.ISAAC.2023.29,
  author =	{Englert, Matthias and Matsakis, Nicolaos and Vesel\'{y}, Pavel},
  title =	{{Approximation Guarantees for Shortest Superstrings: Simpler and Better}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{29:1--29:17},
  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.2023.29},
  URN =		{urn:nbn:de:0030-drops-193319},
  doi =		{10.4230/LIPIcs.ISAAC.2023.29},
  annote =	{Keywords: Shortest Superstring problem, Approximation Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
Breaking the Barrier Of 2 for the Competitiveness of Longest Queue Drop

Authors: Antonios Antoniadis, Matthias Englert, Nicolaos Matsakis, and Pavel Veselý

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


Abstract
We consider the problem of managing the buffer of a shared-memory switch that transmits packets of unit value. A shared-memory switch consists of an input port, a number of output ports, and a buffer with a specific capacity. In each time step, an arbitrary number of packets arrive at the input port, each packet designated for one output port. Each packet is added to the queue of the respective output port. If the total number of packets exceeds the capacity of the buffer, some packets have to be irrevocably rejected. At the end of each time step, each output port transmits a packet in its queue and the goal is to maximize the number of transmitted packets. The Longest Queue Drop (LQD) online algorithm accepts any arriving packet to the buffer. However, if this results in the buffer exceeding its memory capacity, then LQD drops a packet from the back of whichever queue is currently the longest, breaking ties arbitrarily. The LQD algorithm was first introduced in 1991, and is known to be 2-competitive since 2001. Although LQD remains the best known online algorithm for the problem and is of practical interest, determining its true competitiveness is a long-standing open problem. We show that LQD is 1.707-competitive, establishing the first (2-ε) upper bound for the competitive ratio of LQD, for a constant ε > 0.

Cite as

Antonios Antoniadis, Matthias Englert, Nicolaos Matsakis, and Pavel Veselý. Breaking the Barrier Of 2 for the Competitiveness of Longest Queue Drop. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 17:1-17:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{antoniadis_et_al:LIPIcs.ICALP.2021.17,
  author =	{Antoniadis, Antonios and Englert, Matthias and Matsakis, Nicolaos and Vesel\'{y}, Pavel},
  title =	{{Breaking the Barrier Of 2 for the Competitiveness of Longest Queue Drop}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{17:1--17:20},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.17},
  URN =		{urn:nbn:de:0030-drops-140864},
  doi =		{10.4230/LIPIcs.ICALP.2021.17},
  annote =	{Keywords: buffer management, online scheduling, online algorithms, longest queue drop}
}
Document
Reachability in Fixed Dimension Vector Addition Systems with States

Authors: Wojciech Czerwiński, Sławomir Lasota, Ranko Lazić, Jérôme Leroux, and Filip Mazowiecki

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)


Abstract
The reachability problem is a central decision problem in verification of vector addition systems with states (VASS). In spite of recent progress, the complexity of the reachability problem remains unsettled, and it is closely related to the lengths of shortest VASS runs that witness reachability. We obtain three main results for VASS of fixed dimension. For the first two, we assume that the integers in the input are given in unary, and that the control graph of the given VASS is flat (i.e., without nested cycles). We obtain a family of VASS in dimension 3 whose shortest runs are exponential, and we show that the reachability problem is NP-hard in dimension 7. These results resolve negatively questions that had been posed by the works of Blondin et al. in LICS 2015 and Englert et al. in LICS 2016, and contribute a first construction that distinguishes 3-dimensional flat VASS from 2-dimensional ones. Our third result, by means of a novel family of products of integer fractions, shows that 4-dimensional VASS can have doubly exponentially long shortest runs. The smallest dimension for which this was previously known is 14.

Cite as

Wojciech Czerwiński, Sławomir Lasota, Ranko Lazić, Jérôme Leroux, and Filip Mazowiecki. Reachability in Fixed Dimension Vector Addition Systems with States. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 48:1-48:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{czerwinski_et_al:LIPIcs.CONCUR.2020.48,
  author =	{Czerwi\'{n}ski, Wojciech and Lasota, S{\l}awomir and Lazi\'{c}, Ranko and Leroux, J\'{e}r\^{o}me and Mazowiecki, Filip},
  title =	{{Reachability in Fixed Dimension Vector Addition Systems with States}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{48:1--48:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.48},
  URN =		{urn:nbn:de:0030-drops-128605},
  doi =		{10.4230/LIPIcs.CONCUR.2020.48},
  annote =	{Keywords: reachability problem, vector addition systems, Petri nets}
}
Document
Invited Talk
Finkel Was Right: Counter-Examples to Several Conjectures on Variants of Vector Addition Systems (Invited Talk)

Authors: Ranko Lazić

Published in: LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)


Abstract
Studying one-dimensional grammar vector addition systems has long been advocated by Alain Finkel. In this presentation, we shall see how research on those systems has led to the recent breakthrough tower lower bound for the reachability problem on vector addition systems, obtained by Czerwiński et al. In fact, we shall look at how appropriate modifications of an underlying technical construction can lead to counter-examples to several conjectures on one-dimensional grammar vector addition systems, fixed-dimensional vector addition systems, and fixed-dimensional flat vector addition systems.

Cite as

Ranko Lazić. Finkel Was Right: Counter-Examples to Several Conjectures on Variants of Vector Addition Systems (Invited Talk). In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 3:1-3:2, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


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@InProceedings{lazic:LIPIcs.FSTTCS.2019.3,
  author =	{Lazi\'{c}, Ranko},
  title =	{{Finkel Was Right: Counter-Examples to Several Conjectures on Variants of Vector Addition Systems}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{3:1--3:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Chattopadhyay, Arkadev and Gastin, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.3},
  URN =		{urn:nbn:de:0030-drops-115653},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.3},
  annote =	{Keywords: Petri nets, vector addition systems, reachability}
}
Document
New Pumping Technique for 2-Dimensional VASS

Authors: Wojciech Czerwiński, Sławomir Lasota, Christof Löding, and Radosław Piórkowski

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
We propose a new pumping technique for 2-dimensional vector addition systems with states (2-VASS) building on natural geometric properties of runs. We illustrate its applicability by reproving an exponential bound on the length of the shortest accepting run, and by proving a new pumping lemma for languages of 2-VASS. The technique is expected to be useful for settling questions concerning languages of 2-VASS, e.g., for establishing decidability status of the regular separability problem.

Cite as

Wojciech Czerwiński, Sławomir Lasota, Christof Löding, and Radosław Piórkowski. New Pumping Technique for 2-Dimensional VASS. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 62:1-62:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{czerwinski_et_al:LIPIcs.MFCS.2019.62,
  author =	{Czerwi\'{n}ski, Wojciech and Lasota, S{\l}awomir and L\"{o}ding, Christof and Pi\'{o}rkowski, Rados{\l}aw},
  title =	{{New Pumping Technique for 2-Dimensional VASS}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{62:1--62:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.62},
  URN =		{urn:nbn:de:0030-drops-110066},
  doi =		{10.4230/LIPIcs.MFCS.2019.62},
  annote =	{Keywords: vector addition systems with states, pumping, decidability}
}
Document
Reachability for Bounded Branching VASS

Authors: Filip Mazowiecki and Michał Pilipczuk

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)


Abstract
In this paper we consider the reachability problem for bounded branching VASS. Bounded VASS are a variant of the classic VASS model where all values in all configurations are upper bounded by a fixed natural number, encoded in binary in the input. This model gained a lot of attention in 2012 when Haase et al. showed its connections with timed automata. Later in 2013 Fearnley and Jurdziński proved that the reachability problem in this model is PSPACE-complete even in dimension 1. Here, we investigate the complexity of the reachability problem when the model is extended with branching transitions, and we prove that the problem is EXPTIME-complete when the dimension is 2 or larger.

Cite as

Filip Mazowiecki and Michał Pilipczuk. Reachability for Bounded Branching VASS. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 28:1-28:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{mazowiecki_et_al:LIPIcs.CONCUR.2019.28,
  author =	{Mazowiecki, Filip and Pilipczuk, Micha{\l}},
  title =	{{Reachability for Bounded Branching VASS}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{28:1--28:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.28},
  URN =		{urn:nbn:de:0030-drops-109303},
  doi =		{10.4230/LIPIcs.CONCUR.2019.28},
  annote =	{Keywords: Branching VASS, counter machines, reachability problem, bobrvass}
}
Document
Invited Talk
Petri Net Reachability Problem (Invited Talk)

Authors: Jérôme Leroux

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. In this presentation, we overview decidability and complexity results over the last fifty years about the Petri net reachability problem.

Cite as

Jérôme Leroux. Petri Net Reachability Problem (Invited Talk). In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 5:1-5:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{leroux:LIPIcs.MFCS.2019.5,
  author =	{Leroux, J\'{e}r\^{o}me},
  title =	{{Petri Net Reachability Problem}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{5:1--5:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.5},
  URN =		{urn:nbn:de:0030-drops-109493},
  doi =		{10.4230/LIPIcs.MFCS.2019.5},
  annote =	{Keywords: Petri net, Reachability problem, Formal verification, Concurrency}
}
Document
Online Makespan Scheduling with Job Migration on Uniform Machines

Authors: Matthias Englert, David Mezlaf, and Matthias Westermann

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)


Abstract
In the classic minimum makespan scheduling problem, we are given an input sequence of n jobs with sizes. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we allow the online algorithm to reassign up to k jobs to different machines in the final assignment. For m identical machines, Albers and Hellwig (Algorithmica, 2017) give tight bounds on the competitive ratio in this model. The precise ratio depends on, and increases with, m. It lies between 4/3 and ~~ 1.4659. They show that k = O(m) is sufficient to achieve this bound and no k = o(n) can result in a better bound. We study m uniform machines, i.e., machines with different speeds, and show that this setting is strictly harder. For sufficiently large m, there is a delta = Theta(1) such that, for m machines with only two different machine speeds, no online algorithm can achieve a competitive ratio of less than 1.4659 + delta with k = o(n). We present a new algorithm for the uniform machine setting. Depending on the speeds of the machines, our scheduling algorithm achieves a competitive ratio that lies between 4/3 and ~~ 1.7992 with k = O(m). We also show that k = Omega(m) is necessary to achieve a competitive ratio below 2. Our algorithm is based on a subtle imbalance with respect to the completion times of the machines, complemented by a bicriteria approximation algorithm that minimizes the makespan and maximizes the average completion time for certain sets of machines.

Cite as

Matthias Englert, David Mezlaf, and Matthias Westermann. Online Makespan Scheduling with Job Migration on Uniform Machines. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 26:1-26:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{englert_et_al:LIPIcs.ESA.2018.26,
  author =	{Englert, Matthias and Mezlaf, David and Westermann, Matthias},
  title =	{{Online Makespan Scheduling with Job Migration on Uniform Machines}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{26:1--26:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.26},
  URN =		{urn:nbn:de:0030-drops-94890},
  doi =		{10.4230/LIPIcs.ESA.2018.26},
  annote =	{Keywords: online algorithms, competitive analysis, minimum makespan scheduling, job migration}
}
Document
Dynamic Sketching for Graph Optimization Problems with Applications to Cut-Preserving Sketches

Authors: Sepehr Assadi, Sanjeev Khanna, Yang Li, and Val Tannen

Published in: LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)


Abstract
In this paper, we introduce a new model for sublinear algorithms called dynamic sketching. In this model, the underlying data is partitioned into a large static part and a small dynamic part and the goal is to compute a summary of the static part (i.e, a sketch) such that given any update for the dynamic part, one can combine it with the sketch to compute a given function. We say that a sketch is compact if its size is bounded by a polynomial function of the length of the dynamic data, (essentially) independent of the size of the static part. A graph optimization problem P in this model is defined as follows. The input is a graph G(V,E) and a set T \subseteq V of k terminals; the edges between the terminals are the dynamic part and the other edges in G are the static part. The goal is to summarize the graph G into a compact sketch (of size poly(k)) such that given any set Q of edges between the terminals, one can answer the problem P for the graph obtained by inserting all edges in Q to G, using only the sketch. We study the fundamental problem of computing a maximum matching and prove tight bounds on the sketch size. In particular, we show that there exists a (compact) dynamic sketch of size O(k^2) for the matching problem and any such sketch has to be of size \Omega(k^2). Our sketch for matchings can be further used to derive compact dynamic sketches for other fundamental graph problems involving cuts and connectivities. Interestingly, our sketch for matchings can also be used to give an elementary construction of a cut-preserving vertex sparsifier with space O(kC^2) for k-terminal graphs, which matches the best known upper bound; here C is the total capacity of the edges incident on the terminals. Additionally, we give an improved lower bound (in terms of C) of Omega(C/log{C}) on size of cut-preserving vertex sparsifiers, and establish that progress on dynamic sketching of the s-t max-flow problem (either upper bound or lower bound) immediately leads to better bounds for size of cut-preserving vertex sparsifiers.

Cite as

Sepehr Assadi, Sanjeev Khanna, Yang Li, and Val Tannen. Dynamic Sketching for Graph Optimization Problems with Applications to Cut-Preserving Sketches. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 52-68, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{assadi_et_al:LIPIcs.FSTTCS.2015.52,
  author =	{Assadi, Sepehr and Khanna, Sanjeev and Li, Yang and Tannen, Val},
  title =	{{Dynamic Sketching for Graph Optimization Problems with Applications to Cut-Preserving Sketches}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{52--68},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Harsha, Prahladh and Ramalingam, G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.52},
  URN =		{urn:nbn:de:0030-drops-56361},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.52},
  annote =	{Keywords: Small-space Algorithms, Maximum Matchings, Vertex Sparsifiers}
}
Document
Terminal Embeddings

Authors: Michael Elkin, Arnold Filtser, and Ofer Neiman

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)


Abstract
In this paper we study terminal embeddings, in which one is given a finite metric (X,d_X) (or a graph G=(V,E)) and a subset K of X of its points are designated as terminals. The objective is to embed the metric into a normed space, while approximately preserving all distances among pairs that contain a terminal. We devise such embeddings in various settings, and conclude that even though we have to preserve approx |K| * |X| pairs, the distortion depends only on |K|, rather than on |X|. We also strengthen this notion, and consider embeddings that approximately preserve the distances between all pairs, but provide improved distortion for pairs containing a terminal. Surprisingly, we show that such embeddings exist in many settings, and have optimal distortion bounds both with respect to X \times X and with respect to K * X. Moreover, our embeddings have implications to the areas of Approximation and Online Algorithms. In particular, Arora et. al. devised an ~O(sqrt(log(r))-approximation algorithm for sparsest-cut instances with r demands. Building on their framework, we provide an ~O(sqrt(log |K|)-approximation for sparsest-cut instances in which each demand is incident on one of the vertices of K (aka, terminals). Since |K| <= r, our bound generalizes that of Arora et al.

Cite as

Michael Elkin, Arnold Filtser, and Ofer Neiman. Terminal Embeddings. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 242-264, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{elkin_et_al:LIPIcs.APPROX-RANDOM.2015.242,
  author =	{Elkin, Michael and Filtser, Arnold and Neiman, Ofer},
  title =	{{Terminal Embeddings}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{242--264},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.242},
  URN =		{urn:nbn:de:0030-drops-53064},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.242},
  annote =	{Keywords: embedding, distortion, terminals}
}
Document
Generalized Reordering Buffer Management

Authors: Yossi Azar, Matthias Englert, Iftah Gamzu, and Eytan Kidron

Published in: LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)


Abstract
An instance of the generalized reordering buffer management problem consists of a service station that has k servers, each configured with a color, and a buffer of size b. The station needs to serve an online stream of colored items. Whenever an item arrives, it is stored in the buffer. At any point in time, a currently pending item can be served by switching a server to its color. The objective is to serve all items in a way that minimizes the number of servers color switches. This problem generalizes two well-studied online problems: the paging problem, which is the special case when b=1, and the reordering buffer problem, which is the special case when k=1. In this paper, we develop a randomized online algorithm that obtains a competitive ratio of O(sqrt(b).ln(k)). Note that this result beats the easy deterministic lower bound of k whenever b < k^(2-e). We complement our randomized approach by presenting a deterministic algorithm that attains a competitive ratio of O(min{k^2.ln(b),k.b}). We further demonstrate that if our deterministic algorithm can employ k/(1-d) servers where d is in (0,1), then it achieves a competitive ratio of O(min{ln(b/d^2),b/d}) against an optimal offline adversary that employs k servers.

Cite as

Yossi Azar, Matthias Englert, Iftah Gamzu, and Eytan Kidron. Generalized Reordering Buffer Management. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 87-98, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)


Copy BibTex To Clipboard

@InProceedings{azar_et_al:LIPIcs.STACS.2014.87,
  author =	{Azar, Yossi and Englert, Matthias and Gamzu, Iftah and Kidron, Eytan},
  title =	{{Generalized Reordering Buffer Management}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{87--98},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Mayr, Ernst W. and Portier, Natacha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.87},
  URN =		{urn:nbn:de:0030-drops-44498},
  doi =		{10.4230/LIPIcs.STACS.2014.87},
  annote =	{Keywords: online algorithms, paging, reordering buffer}
}
Document
Economical Caching

Authors: Matthias Englert, Heiko Röglin, Jacob Spönemann, and Berthold Vöcking

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)


Abstract
We study the management of buffers and storages in environments with unpredictably varying prices in a competitive analysis. In the economical caching problem, there is a storage with a certain capacity. For each time step, an online algorithm is given a price from the interval $[1,\alpha]$, a consumption, and possibly a buying limit. The online algorithm has to decide the amount to purchase from some commodity, knowing the parameter $\alpha$ but without knowing how the price evolves in the future. The algorithm can purchase at most the buying limit. If it purchases more than the current consumption, then the excess is stored in the storage; otherwise, the gap between consumption and purchase must be taken from the storage. The goal is to minimize the total cost. Interesting applications are, for example, stream caching on mobile devices with different classes of service, battery management in micro hybrid cars, and the efficient purchase of resources. First we consider the simple but natural class of algorithms that can informally be described as memoryless. We show that these algorithms cannot achieve a competitive ratio below $\sqrt{\alpha}$. Then we present a more sophisticated deterministic algorithm achieving a competitive ratio of \[\textstyle \frac{1}{W\left(\frac{1-\alpha}{e\alpha}\right)+1} \in \left[\frac{\sqrt{\alpha}}{\sqrt{2}}, \frac{\sqrt{\alpha}+1}{\sqrt{2}} \right] \enspace, \] where $W$ denotes the Lambert~W function. We prove that this algorithm is optimal and that not even randomized online algorithms can achieve a better competitive ratio. On the other hand, we show how to achieve a constant competitive ratio if the storage capacity of the online algorithm exceeds the storage capacity of an optimal offline algorithm by a factor of $\log \alpha$.

Cite as

Matthias Englert, Heiko Röglin, Jacob Spönemann, and Berthold Vöcking. Economical Caching. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 385-396, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)


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@InProceedings{englert_et_al:LIPIcs.STACS.2009.1826,
  author =	{Englert, Matthias and R\"{o}glin, Heiko and Sp\"{o}nemann, Jacob and V\"{o}cking, Berthold},
  title =	{{Economical Caching}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{385--396},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1826},
  URN =		{urn:nbn:de:0030-drops-18263},
  doi =		{10.4230/LIPIcs.STACS.2009.1826},
  annote =	{Keywords: Online algorithms, Competitive analysis, Storage management}
}
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