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Documents authored by Fiat, Amos

Document
DOI: 10.4230/LIPIcs.ESA.2026.55
Multi Choice Min Prophet

Authors: Yossi Azar, Itamar Biran, and Amos Fiat

Published in: LIPIcs, Volume 388, 34th Annual European Symposium on Algorithms (ESA 2026)

Abstract
The prophet inequality is a fundamental problem in optimal stopping theory. Given n independent variables drawn from known distributions, a player observes values sequentially and must decide irrevocably whether to stop and accept the current value or continue. The goal is to select a single element while maximizing the ratio between the value chosen and that of the maximum value in the sequence. In this paper, we study the minimization counterpart, often termed the min prophet or cost prophet inequality. Unlike the maximization setting, where simple threshold algorithms achieve half of the prophet’s value, the minimization setting is significantly harder, with an exponential lower bound even for i.i.d. variables. We study a multi-choice relaxation in which the algorithm may select multiple variables and gets to choose the best amongst them (the minimum amongst those selected). Our goal is to minimize the expected number of selections while achieving a constant competitive ratio. For adversarial order, we show that a constant competitive ratio requires a nearly linear number of choices in expectation, ergo, Ω(n/ln n). In contrast, we show that for the prophet secretary model (random order) one can attain constant competitiveness while requiring only an exponentially smaller expected number of choices i.e. O(ln n). We give a refined analysis and define M to be the ratio of the minimum expected value of any single variable to the expected minimum value of all variables (the prophet’s value) and present an algorithm that achieves a constant competitive ratio with O(min{ln ln M, ln n}) choices in expectation for the prophet secretary. We show that this is tight up to low order log factors even for the special case of the i.i.d. model. Specifically, the lower bound on the expected number of choices for any constant competitive algorithm is Ω(min{ln ln M/ln ln ln M, ln n/ln ln n}). We also show that if we insist on a deterministic bound on the number of choices then every constant competitive algorithm requires n choices. This holds even in the i.i.d. setting and shows that to achieve a constant competitive algorithm there is an exponential gap between the lower bound on the deterministic number of choices and the upper bound on the expected number of choices. Finally, we consider a variant where both the algorithm and the adversary choose r values and pay their sum, this is the minimization multi unit version. We extend our techniques to the multi-unit variant for i.i.d. variables, achieving a constant competitive ratio with a small expected number of choices.
Cite as

Yossi Azar, Itamar Biran, and Amos Fiat. Multi Choice Min Prophet. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 55:1-55:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{azar_et_al:LIPIcs.ESA.2026.55,
  author =	{Azar, Yossi and Biran, Itamar and Fiat, Amos},
  title =	{{Multi Choice Min Prophet}},
  booktitle =	{34th Annual European Symposium on Algorithms (ESA 2026)},
  pages =	{55:1--55:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-445-1},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{388},
  editor =	{Bille, Philip and Pettie, Seth and Storandt, Sabine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2026.55},
  URN =		{urn:nbn:de:0030-drops-271917},
  doi =		{10.4230/LIPIcs.ESA.2026.55},
  annote =	{Keywords: Prophet inequalities, Min Cost, Multiple choice, Multi Unit}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.10
Dynamic Pricing of Servers on Trees

Authors: Ilan Reuven Cohen, Alon Eden, Amos Fiat, and Łukasz Jeż

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
In this paper we consider the k-server problem where events are generated by selfish agents, known as the selfish k-server problem. In this setting, there is a set of k servers located in some metric space. Selfish agents arrive in an online fashion, each has a request located on some point in the metric space, and seeks to serve his request with the server of minimum distance to the request. If agents choose to serve their request with the nearest server, this mimics the greedy algorithm which has an unbounded competitive ratio. We propose an algorithm that associates a surcharge with each server independently of the agent to arrive (and therefore, yields a truthful online mechanism). An agent chooses to serve his request with the server that minimizes the distance to the request plus the associated surcharge to the server. This paper extends [Ilan Reuven Cohen et al., 2015], which gave an optimal k-competitive dynamic pricing scheme for the selfish k-server problem on the line. We give a k-competitive dynamic pricing algorithm for the selfish k-server problem on tree metric spaces, which matches the optimal online (non truthful) algorithm. We show that an alpha-competitive dynamic pricing scheme exists on the tree if and only if there exists alpha-competitive online algorithm on the tree that is lazy and monotone. Given this characterization, the main technical difficulty is coming up with such an online algorithm.
Cite as

Ilan Reuven Cohen, Alon Eden, Amos Fiat, and Łukasz Jeż. Dynamic Pricing of Servers on Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{cohen_et_al:LIPIcs.APPROX-RANDOM.2019.10,
  author =	{Cohen, Ilan Reuven and Eden, Alon and Fiat, Amos and Je\.{z}, {\L}ukasz},
  title =	{{Dynamic Pricing of Servers on Trees}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{10:1--10:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.10},
  URN =		{urn:nbn:de:0030-drops-112252},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.10},
  annote =	{Keywords: Online algorithms, Online mechanisms, k-server problem, Online pricing}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.27
Truthful Prompt Scheduling for Minimizing Sum of Completion Times

Authors: Alon Eden, Michal Feldman, Amos Fiat, and Tzahi Taub

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

Abstract
We give a prompt online mechanism for minimizing the sum of [weighted] completion times. This is the first prompt online algorithm for the problem. When such jobs are strategic agents, delaying scheduling decisions makes little sense. Moreover, the mechanism has a particularly simple form of an anonymous menu of options.
Cite as

Alon Eden, Michal Feldman, Amos Fiat, and Tzahi Taub. Truthful Prompt Scheduling for Minimizing Sum of Completion Times. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{eden_et_al:LIPIcs.ESA.2018.27,
  author =	{Eden, Alon and Feldman, Michal and Fiat, Amos and Taub, Tzahi},
  title =	{{Truthful Prompt Scheduling for Minimizing Sum of Completion Times}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{27:1--27:14},
  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.2018.27},
  URN =		{urn:nbn:de:0030-drops-94905},
  doi =		{10.4230/LIPIcs.ESA.2018.27},
  annote =	{Keywords: Scheduling, Mechanism design, Online algorithms}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.43
Carpooling in Social Networks

Authors: Amos Fiat, Anna R. Karlin, Elias Koutsoupias, Claire Mathieu, and Rotem Zach

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

Abstract
We consider the online carpool fairness problem of [Fagin and Williams, 1983] in which an online algorithm is presented with a sequence of pairs drawn from a group of n potential drivers. The online algorithm must select one driver from each pair, with the objective of partitioning the driving burden as fairly as possible for all drivers. The unfairness of an online algorithm is a measure of the worst-case deviation between the number of times a person has driven and the number of times they would have driven if life was completely fair. We introduce a version of the problem in which drivers only carpool with their neighbors in a given social network graph; this is a generalization of the original problem, which corresponds to the social network of the complete graph. We show that for graphs of degree d, the unfairness of deterministic algorithms against adversarial sequences is exactly d/2. For random sequences of edges from planar graph social networks we give a [deterministic] algorithm with logarithmic unfairness (holds more generally for any bounded-genus graph). This does not follow from previous random sequence results in the original model, as we show that restricting the random sequences to sparse social network graphs may increase the unfairness. A very natural class of randomized online algorithms are so-called static algorithms that preserve the same state distribution over time. Surprisingly, we show that any such algorithm has unfairness ~Theta(sqrt(d)) against oblivious adversaries. This shows that the local random greedy algorithm of [Ajtai et al, 1996] is close to optimal amongst the class of static algorithms. A natural (non-static) algorithm is global random greedy (which acts greedily and breaks ties at random). We improve the lower bound on the competitive ratio from Omega(log^{1/3}(d)) to Omega(log(d)). We also show that the competitive ratio of global random greedy against adaptive adversaries is Omega(d).
Cite as

Amos Fiat, Anna R. Karlin, Elias Koutsoupias, Claire Mathieu, and Rotem Zach. Carpooling in Social Networks. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 43:1-43:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{fiat_et_al:LIPIcs.ICALP.2016.43,
  author =	{Fiat, Amos and Karlin, Anna R. and Koutsoupias, Elias and Mathieu, Claire and Zach, Rotem},
  title =	{{Carpooling in Social Networks}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{43:1--43:13},
  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.2016.43},
  URN =		{urn:nbn:de:0030-drops-63234},
  doi =		{10.4230/LIPIcs.ICALP.2016.43},
  annote =	{Keywords: Online algorithms, Fairness, Randomized algorithms, Competitive ratio, Carpool problem}
}
Document
DOI: 10.4230/DagSemProc.07261.12
Strong Price of Anarchy for Machine Load Balancing

Authors: Amos Fiat, Meital Levy, Haim Kaplan, and Svetlana Olonetsky

Published in: Dagstuhl Seminar Proceedings, Volume 7261, Fair Division (2007)

Abstract
As defined by Aumann in 1959, a strong equilibrium is a Nash equilibrium that is resilient to deviations by coalitions. We give tight bounds on the strong price of anarchy for load balancing on related machines. We also give tight bounds for $k$-strong equilibria, where the size of a deviating coalition is at most $k$, for unrelated machines.
Cite as

Amos Fiat, Meital Levy, Haim Kaplan, and Svetlana Olonetsky. Strong Price of Anarchy for Machine Load Balancing. In Fair Division. Dagstuhl Seminar Proceedings, Volume 7261, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{fiat_et_al:DagSemProc.07261.12,
  author =	{Fiat, Amos and Levy, Meital and Kaplan, Haim and Olonetsky, Svetlana},
  title =	{{Strong Price of Anarchy  for  Machine Load Balancing}},
  booktitle =	{Fair Division},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7261},
  editor =	{Steven Brams and Kirk Pruhs and Gerhard Woeginger},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07261.12},
  URN =		{urn:nbn:de:0030-drops-12256},
  doi =		{10.4230/DagSemProc.07261.12},
  annote =	{Keywords: Game theory, Strong Nash equilibria, Load balancing, Price of Anarchy}
}
Document
DOI: 10.4230/DagSemRep.347
Online Algorithms (Dagstuhl Seminar 02271)

Authors: Susanne Albers, Amos Fiat, and Gerhard J. Woeginger

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Susanne Albers, Amos Fiat, and Gerhard J. Woeginger. Online Algorithms (Dagstuhl Seminar 02271). Dagstuhl Seminar Report 347, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2002)

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@TechReport{albers_et_al:DagSemRep.347,
  author =	{Albers, Susanne and Fiat, Amos and Woeginger, Gerhard J.},
  title =	{{Online Algorithms (Dagstuhl Seminar 02271)}},
  pages =	{1--20},
  ISSN =	{1619-0203},
  year =	{2002},
  type = 	{Dagstuhl Seminar Report},
  number =	{347},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.347},
  URN =		{urn:nbn:de:0030-drops-152281},
  doi =		{10.4230/DagSemRep.347},
}
Document
DOI: 10.4230/DagSemRep.243
Competitive Algorithms (Dagstuhl Seminar 99251)

Authors: Amos Fiat, Anna Karlin, and Gerhard Woeginger

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Amos Fiat, Anna Karlin, and Gerhard Woeginger. Competitive Algorithms (Dagstuhl Seminar 99251). Dagstuhl Seminar Report 243, pp. 1-25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2000)

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@TechReport{fiat_et_al:DagSemRep.243,
  author =	{Fiat, Amos and Karlin, Anna and Woeginger, Gerhard},
  title =	{{Competitive Algorithms (Dagstuhl Seminar 99251)}},
  pages =	{1--25},
  ISSN =	{1619-0203},
  year =	{2000},
  type = 	{Dagstuhl Seminar Report},
  number =	{243},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.243},
  URN =		{urn:nbn:de:0030-drops-151295},
  doi =		{10.4230/DagSemRep.243},
}
Document
DOI: 10.4230/DagSemRep.149
On-line Algorithms (Dagstuhl Seminar 9626)

Authors: Amos Fiat and Gerhard Woeginger

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Amos Fiat and Gerhard Woeginger. On-line Algorithms (Dagstuhl Seminar 9626). Dagstuhl Seminar Report 149, pp. 1-25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1996)

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@TechReport{fiat_et_al:DagSemRep.149,
  author =	{Fiat, Amos and Woeginger, Gerhard},
  title =	{{On-line Algorithms (Dagstuhl Seminar 9626)}},
  pages =	{1--25},
  ISSN =	{1619-0203},
  year =	{1996},
  type = 	{Dagstuhl Seminar Report},
  number =	{149},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.149},
  URN =		{urn:nbn:de:0030-drops-150369},
  doi =		{10.4230/DagSemRep.149},
}

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