Document

APPROX

**Published in:** LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

The online joint replenishment problem (JRP) is a fundamental problem in the area of online problems with delay. Over the last decade, several works have studied generalizations of JRP with different cost functions for servicing requests. Most prior works on JRP and its generalizations have focused on the clairvoyant setting. Recently, Touitou [Noam Touitou, 2023] developed a non-clairvoyant framework that provided an O(√{n log n}) upper bound for a wide class of generalized JRP, where n is the number of request types.
We advance the study of non-clairvoyant algorithms by providing a simpler, modular framework that matches the competitive ratio established by Touitou for the same class of generalized JRP. Our key insight is to leverage universal algorithms for Set Cover to approximate arbitrary monotone subadditive functions using a simple class of functions termed disjoint. This allows us to reduce the problem to several independent instances of the TCP Acknowledgement problem, for which a simple 2-competitive non-clairvoyant algorithm is known. The modularity of our framework is a major advantage as it allows us to tailor the reduction to specific problems and obtain better competitive ratios. In particular, we obtain tight O(√n)-competitive algorithms for two significant problems: Multi-Level Aggregation and Weighted Symmetric Subadditive Joint Replenishment. We also show that, in contrast, Touitou’s algorithm is Ω(√{n log n})-competitive for both of these problems.

Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, and Seeun William Umboh. Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{ezra_et_al:LIPIcs.APPROX/RANDOM.2024.12, author = {Ezra, Tomer and Leonardi, Stefano and Paw{\l}owski, Micha{\l} and Russo, Matteo and Umboh, Seeun William}, title = {{Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)}, pages = {12:1--12:24}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-348-5}, ISSN = {1868-8969}, year = {2024}, volume = {317}, editor = {Kumar, Amit and Ron-Zewi, Noga}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.12}, URN = {urn:nbn:de:0030-drops-210050}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2024.12}, annote = {Keywords: Set Cover, Joint Replenishment, TCP-Acknowledgment, Subadditive Function Approximation, Multi-Level Aggregation} }

Document

Complete Volume

**Published in:** LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

LIPIcs, Volume 132, ICALP'19, Complete Volume

46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@Proceedings{baier_et_al:LIPIcs.ICALP.2019, title = {{LIPIcs, Volume 132, ICALP'19, Complete Volume}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019}, URN = {urn:nbn:de:0030-drops-108644}, doi = {10.4230/LIPIcs.ICALP.2019}, annote = {Keywords: Theory of computation} }

Document

Front Matter

**Published in:** LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Front Matter, Table of Contents, Preface, Conference Organization

46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 0:i-0:xxxviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{baier_et_al:LIPIcs.ICALP.2019.0, author = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {0:i--0:xxxviii}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.0}, URN = {urn:nbn:de:0030-drops-105765}, doi = {10.4230/LIPIcs.ICALP.2019.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

Document

Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management

**Published in:** LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Exploring large-scale networks is a time consuming and expensive task which is usually operated in a complex and uncertain environment. A crucial aspect of network exploration is the development of suitable strategies that decide which nodes and edges to probe at each stage of the process.
To model this process, we introduce the stochastic graph exploration problem. The input is an undirected graph G=(V,E) with a source vertex s, stochastic edge costs drawn from a distribution pi_e, e in E, and rewards on vertices of maximum value R. The goal is to find a set F of edges of total cost at most B such that the subgraph of G induced by F is connected, contains s, and maximizes the total reward. This problem generalizes the stochastic knapsack problem and other stochastic probing problems recently studied.
Our focus is on the development of efficient nonadaptive strategies that are competitive against the optimal adaptive strategy. A major challenge is the fact that the problem has an Omega(n) adaptivity gap even on a tree of n vertices. This is in sharp contrast with O(1) adaptivity gap of the stochastic knapsack problem, which is a special case of our problem. We circumvent this negative result by showing that O(log nR) resource augmentation suffices to obtain O(1) approximation on trees and O(log nR) approximation on general graphs. To achieve this result, we reduce stochastic graph exploration to a memoryless process - the minesweeper problem - which assigns to every edge a probability that the process terminates when the edge is probed. For this problem, interesting in its own, we present an optimal polynomial time algorithm on trees and an O(log nR) approximation for general graphs.
We study also the problem in which the maximum cost of an edge is a logarithmic fraction of the budget. We show that under this condition, there exist polynomial-time oblivious strategies that use 1+epsilon budget, whose adaptivity gaps on trees and general graphs are 1+epsilon and 8+epsilon, respectively. Finally, we provide additional results on the structure and the complexity of nonadaptive and adaptive strategies.

Aris Anagnostopoulos, Ilan R. Cohen, Stefano Leonardi, and Jakub Łącki. Stochastic Graph Exploration. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 136:1-136:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{anagnostopoulos_et_al:LIPIcs.ICALP.2019.136, author = {Anagnostopoulos, Aris and Cohen, Ilan R. and Leonardi, Stefano and {\L}\k{a}cki, Jakub}, title = {{Stochastic Graph Exploration}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {136:1--136:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.136}, URN = {urn:nbn:de:0030-drops-107122}, doi = {10.4230/LIPIcs.ICALP.2019.136}, annote = {Keywords: stochastic optimization, graph exploration, approximation algorithms} }

Document

Complete Volume

**Published in:** LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)

LIPIcs, Volume 100, FUN'18, Complete Volume

9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@Proceedings{ito_et_al:LIPIcs.FUN.2018, title = {{LIPIcs, Volume 100, FUN'18, Complete Volume}}, booktitle = {9th International Conference on Fun with Algorithms (FUN 2018)}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-067-5}, ISSN = {1868-8969}, year = {2018}, volume = {100}, editor = {Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018}, URN = {urn:nbn:de:0030-drops-89311}, doi = {10.4230/LIPIcs.FUN.2018}, annote = {Keywords: Theory of computation, Complexity classes, Algorithm design techniques, Computability, Approximation algorithms analysis, Mathematics of computing} }

Document

Front Matter

**Published in:** LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)

Front Matter, Table of Contents, Preface, Conference Organization

9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 0:i-0:xi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{ito_et_al:LIPIcs.FUN.2018.0, author = {Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {9th International Conference on Fun with Algorithms (FUN 2018)}, pages = {0:i--0:xi}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-067-5}, ISSN = {1868-8969}, year = {2018}, volume = {100}, editor = {Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.0}, URN = {urn:nbn:de:0030-drops-87914}, doi = {10.4230/LIPIcs.FUN.2018.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

Document

**Published in:** LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Consider the following variant of the set cover problem. We are given a universe U={1,...,n} and a collection of subsets C = {S_1,...,S_m} where each S_i is a subset of U. For every element u from U we need to find a set phi(u) from collection C such that u belongs to phi(u). Once we construct and fix the mapping phi from U to C a subset X from the universe U is revealed, and we need to cover all elements from X with exactly phi(X), that is {phi(u)}_{all u from X}. The goal is to find a mapping such that the cover phi(X) is as cheap as possible.
This is an example of a universal problem where the solution has to be created before the actual instance to deal with is revealed. Such problems appear naturally in some settings when we need to optimize under uncertainty and it may be actually too expensive to begin finding a good solution once the input starts being revealed. A rich body of work was devoted to investigate such problems under the regime of worst case analysis, i.e., when we measure how good the solution is by looking at the worst-case ratio: universal solution for a given instance vs optimum solution for the same instance.
As the universal solution is significantly more constrained, it is typical that such a worst-case ratio is actually quite big. One way to give a viewpoint on the problem that would be less vulnerable to such extreme worst-cases is to assume that the instance, for which we will have to create a solution, will be drawn randomly from some probability distribution. In this case one wants to minimize the expected value of the ratio: universal solution vs optimum solution. Here the bounds obtained are indeed smaller than when we compare to the worst-case ratio.
But even in this case we still compare apples to oranges as no universal solution is able to construct the optimum solution for every possible instance. What if we would compare our approximate universal solution against an optimal universal solution that obeys the same rules as we do? We show that under this viewpoint, but still in the stochastic variant, we can indeed obtain better bounds than in the expected ratio model. For example, for the set cover problem we obtain $H_n$ approximation which matches the approximation ratio from the classic deterministic setup. Moreover, we show this for all possible probability distributions over $U$ that have a polynomially large carrier, while all previous results pertained to a model in which elements were sampled independently. Our result is based on rounding a proper configuration IP that captures the optimal universal solution, and using tools from submodular optimization.
The same basic approach leads to improved approximation algorithms for other related problems, including Vertex Cover, Edge Cover, Directed Steiner Tree, Multicut, and Facility Location.

Marek Adamczyk, Fabrizio Grandoni, Stefano Leonardi, and Michal Wlodarczyk. When the Optimum is also Blind: a New Perspective on Universal Optimization. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 35:1-35:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{adamczyk_et_al:LIPIcs.ICALP.2017.35, author = {Adamczyk, Marek and Grandoni, Fabrizio and Leonardi, Stefano and Wlodarczyk, Michal}, title = {{When the Optimum is also Blind: a New Perspective on Universal Optimization}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {35:1--35:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-041-5}, ISSN = {1868-8969}, year = {2017}, volume = {80}, editor = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.35}, URN = {urn:nbn:de:0030-drops-74436}, doi = {10.4230/LIPIcs.ICALP.2017.35}, annote = {Keywords: approximation algorithms, stochastic optimization, submodularity} }

Document

**Published in:** LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Internet display advertising industry follows two main business models. One model is based on direct deals between publishers and advertisers where they sign legal contracts containing terms of fulfillment for a future inventory. The second model is a spot market based on auctioning page views in real-time on advertising exchange (AdX) platforms such as DoubleClick's Ad Exchange, RightMedia, or AppNexus. These exchanges play the role of intermediaries who sell items (e.g. page-views) on behalf of a seller (e.g. a publisher) to buyers (e.g., advertisers) on the opposite side of the market. The computational and economics issues arising in this second model have been extensively investigated in recent times.
In this work, we consider a third emerging model called reservation exchange market. A reservation exchange is a two-sided market between buyer orders for blocks of advertisers' impressions and seller orders for blocks of publishers' page views. The goal is to match seller orders to buyer orders while providing the right incentives to both sides. In this work we first describe the important features of mechanisms for efficient reservation exchange markets. We then address the algorithmic problems of designing revenue sharing schemes to provide a fair division between sellers of the revenue collected from buyers.
A major conceptual contribution of this work is in showing that even though both clinching ascending auctions and VCG mechanisms achieve the same outcome from a buyer perspective, however, from the perspective of revenue sharing among sellers, clinching ascending auctions are much more informative than VCG auctions.

Gagan Goel, Stefano Leonardi, Vahab Mirrokni, Afshin Nikzad, and Renato Paes-Leme. Reservation Exchange Markets for Internet Advertising. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 142:1-142:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{goel_et_al:LIPIcs.ICALP.2016.142, author = {Goel, Gagan and Leonardi, Stefano and Mirrokni, Vahab and Nikzad, Afshin and Paes-Leme, Renato}, title = {{Reservation Exchange Markets for Internet Advertising}}, booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, pages = {142:1--142:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-013-2}, ISSN = {1868-8969}, year = {2016}, volume = {55}, editor = {Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.142}, URN = {urn:nbn:de:0030-drops-62863}, doi = {10.4230/LIPIcs.ICALP.2016.142}, annote = {Keywords: Reservation Markets, Internet Advertising, Two-sided Markets, Clinching Auction, Envy-free allocations} }

Document

**Published in:** LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

In a classical covering problem, we are given a set of requests that we need to satisfy (fully or partially), by buying a subset of items at minimum cost. For example, in the k-MST problem we want to find the cheapest tree spanning at least k nodes of an edge-weighted graph. Here, nodes represent requests whereas edges correspond to items.
In this paper, we initiate the study of a new family of multi-layer covering problems. Each such problem consists of a collection of h distinct instances of a standard covering problem (layers), with the constraint that all layers share the same set of requests. We identify two main subfamilies of these problems:
- in an union multi-layer problem, a request is satisfied if it is satisfied in at least one layer;
- in an intersection multi-layer problem, a request is satisfied if it is satisfied in all layers.
To see some natural applications, consider both generalizations of k-MST. Union k-MST can model a problem where we are asked to connect a set of users to at least one of two communication networks, e.g., a wireless and a wired network. On the other hand, Intersection k-MST can formalize the problem of providing both electricity and water to at least k users.

Marek Cygan, Fabrizio Grandoni, Stefano Leonardi, Marcin Mucha, Marcin Pilipczuk, and Piotr Sankowski. Approximation Algorithms for Union and Intersection Covering Problems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 28-40, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

Copy BibTex To Clipboard

@InProceedings{cygan_et_al:LIPIcs.FSTTCS.2011.28, author = {Cygan, Marek and Grandoni, Fabrizio and Leonardi, Stefano and Mucha, Marcin and Pilipczuk, Marcin and Sankowski, Piotr}, title = {{Approximation Algorithms for Union and Intersection Covering Problems}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)}, pages = {28--40}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-34-7}, ISSN = {1868-8969}, year = {2011}, volume = {13}, editor = {Chakraborty, Supratik and Kumar, Amit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.28}, URN = {urn:nbn:de:0030-drops-33213}, doi = {10.4230/LIPIcs.FSTTCS.2011.28}, annote = {Keywords: Approximation algorithms, Partial covering problems} }

Document

**Published in:** Dagstuhl Seminar Proceedings, Volume 10211, Flexible Network Design (2010)

From Monday 24.05.2010---Friday 28.05.2010, the Dagstuhl Seminar 10211 ``Flexible Network Design '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.

Anupam Gupta, Stefano Leonardi, Berthold Vöcking, and Roger Wattenhofer. 10211 Abstracts Collection – Flexible Network Design. In Flexible Network Design. Dagstuhl Seminar Proceedings, Volume 10211, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

Copy BibTex To Clipboard

@InProceedings{gupta_et_al:DagSemProc.10211.1, author = {Gupta, Anupam and Leonardi, Stefano and V\"{o}cking, Berthold and Wattenhofer, Roger}, title = {{10211 Abstracts Collection – Flexible Network Design}}, booktitle = {Flexible Network Design}, pages = {1--15}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2010}, volume = {10211}, editor = {Anupam Gupta and Stefano Leonardi and Berthold V\"{o}cking and Roger Wattenhofer}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10211.1}, URN = {urn:nbn:de:0030-drops-27279}, doi = {10.4230/DagSemProc.10211.1}, annote = {Keywords: Network Design, Approximation Algorithms, Game Theory and Mechanism Design, Wireless Networks} }

Document

**Published in:** Dagstuhl Seminar Proceedings, Volume 5361, Algorithmic Aspects of Large and Complex Networks (2006)

From 04.09.05 to 09.09.05, the Dagstuhl Seminar 05361 ``Algorithmic Aspects of Large and Complex Networks'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.

Stefano Leonardi, Friedhelm Meyer auf der Heide, and Dorothea Wagner. 05361 Abstracts Collection – Algorithmic Aspects of Large and Complex Networks. In Algorithmic Aspects of Large and Complex Networks. Dagstuhl Seminar Proceedings, Volume 5361, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

Copy BibTex To Clipboard

@InProceedings{leonardi_et_al:DagSemProc.05361.1, author = {Leonardi, Stefano and Meyer auf der Heide, Friedhelm and Wagner, Dorothea}, title = {{05361 Abstracts Collection – Algorithmic Aspects of Large and Complex Networks}}, booktitle = {Algorithmic Aspects of Large and Complex Networks}, pages = {1--19}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2006}, volume = {5361}, editor = {Stefano Leonardi and Friedhelm Meyer auf der Heide and Dorothea Wagner}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05361.1}, URN = {urn:nbn:de:0030-drops-5702}, doi = {10.4230/DagSemProc.05361.1}, annote = {Keywords: Algorithms, Large and Complex Networks} }

Document

**Published in:** Dagstuhl Seminar Proceedings, Volume 5031, Algorithms for Optimization with Incomplete Information (2005)

In this paper we introduce the notion of smoothed competitive analysis of online algorithms. Smoothed analysis has been proposed by Spielman and Teng to explain the behaviour of algorithms that work well in practice while performing very poorly from a worst case analysis point of view. We apply this notion to analyze the Multi-Level Feedback (MLF) algorithm to minimize the total flow time on a sequence of jobs released over time when the processing time of a job is only known at time of completion. The initial processing times are integers in the range $[1,2^K]$. We use a partial bit randomization model, i.e., the initial processing times are smoothed by changing the $k$ least significant bits under a quite general class of probability distributions. We show that MLF admits a smoothed competitive ratio of $O((2^k/\psigma)^3 + (2^k/\psigma)^2 2^{K-k}})$, where $\sigma$ denotes the standard deviation of the distribution. In particular, we obtain a competitive ratio of $O(2^{K-k})$ if $\sigma = \Theta(2^k)$. We also prove an $\Omega(2^{K-k})$ lower bound for any deterministic algorithm that is run on processing times smoothed according to the partial bit randomization model. For various other smoothing models, including the additive symmetric smoothing one, which is a variant of the model used by Spielman and Teng, we give a higher lower bound of $\Omega(2^K)$. A direct consequence of our result is also the first average case analysis of MLF. We show a constant expected ratio of the total flow time of MLF to the optimum under several distributions including the uniform one.

Luca Becchetti, Stefano Leonardi, Alberto Marchetti-Spaccamela, Guidouca Schaefer, and Tjark Vredeveld. Average Case and Smoothed Competitive Analysis of the Multi-Level Feedback Algorithm. In Algorithms for Optimization with Incomplete Information. Dagstuhl Seminar Proceedings, Volume 5031, pp. 5-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

Copy BibTex To Clipboard

@InProceedings{becchetti_et_al:DagSemProc.05031.7, author = {Becchetti, Luca and Leonardi, Stefano and Marchetti-Spaccamela, Alberto and Schaefer, Guidouca and Vredeveld, Tjark}, title = {{Average Case and Smoothed Competitive Analysis of the Multi-Level Feedback Algorithm}}, booktitle = {Algorithms for Optimization with Incomplete Information}, pages = {5--28}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2005}, volume = {5031}, editor = {Susanne Albers and Rolf H. M\"{o}hring and Georg Ch. Pflug and R\"{u}diger Schultz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05031.7}, URN = {urn:nbn:de:0030-drops-752}, doi = {10.4230/DagSemProc.05031.7}, annote = {Keywords: Competitive analysis , average case analysis , smoothed analysis , scheduling} }

X

Feedback for Dagstuhl Publishing

Feedback submitted

Please try again later or send an E-mail