Document

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

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).

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)

Copy BibTex To Clipboard

@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

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

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.

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)

Copy BibTex To Clipboard

@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

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

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.

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)

Copy BibTex To Clipboard

@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

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

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.

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

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

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 $\log \alpha$.

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)

Copy BibTex To Clipboard

@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} }

X

Feedback for Dagstuhl Publishing

Feedback submitted

Please try again later or send an E-mail