Yonatan Aumann

Bar Ilan University, Gan, Tel Aviv, Israel

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Publications (94)31.89 Total impact

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    ABSTRACT: We consider the problem of fairly dividing a two dimensional heterogeneous good among multiple players. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols primarily consider a one-dimensional resource, or allocate each player multiple infinitesimally small "pieces". In practice, however, the two dimensional \emph{shape} of the allotted piece is of crucial importance in many applications (e.g. squares or bounded aspect-ratio rectangles are most useful for building houses, as well as advertisements). We thus introduce and study the problem of fair two-dimensional division wherein the allotted plots must be of some restricted two-dimensional geometric shape(s). Adding this geometric constraint re-opens most questions and challenges related to cake-cutting. Indeed, even the elementary \emph{proportionality} fairness criteria can no longer be guaranteed in all cases. In this paper we thus examine the \emph{level} of proportionality that \emph{can} be guaranteed, providing both impossibility results (for proportionality that cannot be guaranteed), and algorithmic constructions (for proportionality that can be guaranteed). We focus primarily on the case when the cake is a rectilinear polygon and the allotted plots must be squares or bounded aspect-ratio rectangles.
    09/2014;
  • Noam Hazon, Yonatan Aumann, Sarit Kraus, David Sarne
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    ABSTRACT: This paper considers the problem of an agent or a team of agents searching for a resource or tangible good in a physical environment, where the resource or good may possibly be obtained at one of several locations. The cost of acquiring the resource or good at a given location is uncertain (a priori), and the agents can observe the true cost only when physically arriving at this location. Sample applications include agents in exploration and patrol missions (e.g., an agent seeking to find the best location to deploy sensing equipment along its path). The uniqueness of these settings is in that the cost of observing a new location is determined by distance from the current one, impacting the consideration for the optimal search order. Although this model captures many real world scenarios, it has not been investigated so far.We analyze three variants of the problem, differing in their objective: minimizing the total expected cost, maximizing the success probability given an initial budget, and minimizing the budget necessary to obtain a given success probability. For each variant, we first introduce and analyze the problem with a single agent, either providing a polynomial solution to the problem or proving it is NP-complete. We also introduce a fully polynomial time approximation scheme algorithm for the minimum budget variant. In the multi-agent case, we analyze two models for managing resources, shared and private budget models. We present polynomial algorithms that work for any fixed number of agents, in the shared or private budget model. For non-communicating agents in the private budget model, we present a polynomial algorithm that is suitable for any number of agents. We also analyze the difference between homogeneous and heterogeneous agents, both with respect to their allotted resources and with respect to their capabilities. Finally, we define our problem in an environment with self-interested agents. We show how to find a Nash equilibrium in polynomial time, and prove that the bound on the performance of our algorithms, with respect to the social welfare, is tight.
    Artificial Intelligence 03/2013; 196:26–52. · 2.19 Impact Factor
  • Amos Azaria, Yonatan Aumann, Sarit Kraus
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    ABSTRACT: Crowdsourcing applications frequently employ many individual workers, each performing a small amount of work. In such settings, individually determining the reward for each assignment and worker may seem economically beneficial, but is inapplicable if manually performed. We thus consider the problem of designing automated agents for automatic reward determination and negotiation in such settings. We formally describe this problem and show that it is NP-hard. We therefore present two automated agents for the problem, based on two different models of human behavior. The first, the Reservation Price Based Agent (RPBA), is based on the concept of a RP, and the second, the No Bargaining Agent (NBA) which tries to avoid any negotiation. The performance of the agents is tested in extensive experiments with real human subjects, where both NBA and RPBA outperform strategies developed by human experts.
    Autonomous Agents and Multi-Agent Systems 01/2013; · 0.79 Impact Factor
  • Amos Azaria, David Sarner, Yonatan Aumann
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    ABSTRACT: In this paper we study distributed agent matching in environments characterized by costly exploration, where each agent's utility from forming a partnership is influenced by both the maximum and the minimum among the two agent's competence. This kind of utility function is somehow more applicable, compared to the one used in related work that takes the utility to be either the type of the agent partner or "standard" functions such as average or multiplication of the two types. The use of the hybrid min-max utility function is favorable whenever the performance of the agents forming a partnership is principally affected by the most (or least) competent among the two. This paper supplies a cohesive analysis for the min-max case, proving the equilibrium structure for the different min-max linear combination that may be used. We show that in any case that an agent sets its acceptance threshold below its own type it is guaranteed that any agent with a type between this threshold and its own will accept it (the agent) as a partner as well. This result substantially facilitates the calculation of equilibrium for such settings, e.g., when the set of types is finite.
    Proceedings of the The 2012 IEEE/WIC/ACM International Joint Conferences on Web Intelligence and Intelligent Agent Technology - Volume 02; 12/2012
  • David Sarne, Yonatan Aumann
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    ABSTRACT: Humans and software agents alike spend considerable time and effort in searching. Search enables finding the things that better fit and agent's goals. But search can also be a costly process. Search costs can either come in the form of direct monetary payments, or in the form of time and resources spent. In general, the searcher must balance between the benefits provided by longer and broader search, on the one hand, and the associated increased cost, on the other.
    Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 3; 06/2012
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    Yonatan Aumann, Yair Dombb, Avinatan Hassidim
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    ABSTRACT: We consider a setting in which a single divisible good ("cake") needs to be divided between n players, each with a possibly di?fferent valuation function over pieces of the cake. For this setting, we address the problem of ?finding divisions that maximize the social welfare, focusing on divisions where each player needs to get one contiguous piece of the cake. We show that for both the utilitarian and the egalitarian social welfare functions it is NP-hard to find the optimal division. For the utilitarian welfare, we provide a constant factor approximation algorithm, and prove that no FPTAS is possible unless P=NP. For egalitarian welfare, we prove that it is NP-hard to approximate the optimum to any factor smaller than 2. For the case where the number of players is small, we provide an FPT (fixed parameter tractable) FPTAS for both the utilitarian and the egalitarian welfare objectives.
    05/2012;
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    ABSTRACT: We introduce a generalization of interval graphs, which we call dotted interval graphs (DIG). A dotted interval graph is an intersection graph of arithmetic progressions (=dotted intervals). Coloring of dotted intervals graphs naturally arises in the context of high throughput genotyping. We study the properties of dotted interval graphs, with a focus on coloring. We show that any graph is a DIG but that DIG d graphs, i.e. DIGs in which the arithmetic progressions have a jump of at most d, form a strict hierarchy. We show that coloring DIG d graphs is NP-complete even for d = 2. For any fixed d, we provide a 7 8 d approximation for the coloring of DIG d graphs.
    ACM Transactions on Algorithms 01/2012; · 0.54 Impact Factor
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    Orit Arzi, Yonatan Aumann, Yair Dombb
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    ABSTRACT: We consider the problem of fairly dividing a heterogeneous cake between a number of players with different tastes. In this setting, it is known that fairness requirements may result in a suboptimal division from the social welfare standpoint. Here, we show that in some cases, discarding some of the cake and fairly dividing only the remainder may be socially preferable to any fair division of the entire cake. We study this phenomenon, providing asymptotically-tight bounds on the social improvement achievable by such discarding.
    Computing Research Repository - CORR. 01/2011;
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    Orit Arzi, Yonatan Aumann, Yair Dombb
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    ABSTRACT: We consider the problem of fairly dividing a heterogeneous cake between a number of players with different tastes. In this setting, it is known that fairness requirements may result in a suboptimal division from the social welfare standpoint. Here, we show that in some cases, discarding some of the cake and fairly dividing only the remainder may be socially preferable to any fair division of the entire cake. We study this phenomenon, providing asymptotically-tight bounds on the social improvement achievable by such discarding.
    Algorithmic Game Theory, 4th International Symposium, SAGT 2011, Amalfi, Italy, October 17-19, 2011. Proceedings; 01/2011
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    ACM Transactions on Algorithms. 01/2011; 7:24.
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    Yonatan Aumann, Yair Dombb
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    ABSTRACT: We consider the issue of fair division of goods, using the cake cutting abstraction, and aim to bound the possible degradation in social welfare due to the fairness requirements. Previous work has considered this problem for the setting where the division may allocate each player any number of unconnected pieces. Here, we consider the setting where each player must receive a single connected piece. For this setting, we provide tight bounds on the maximum possible degradation to both utilitarian and egalitarian welfare due to three fairness criteria — proportionality, envy-freeness and equitability.
    Internet and Network Economics - 6th International Workshop, WINE 2010, Stanford, CA, USA, December 13-17, 2010. Proceedings; 01/2010
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    Tammar Shrot, Yonatan Aumann, Sarit Kraus
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    ABSTRACT: Coalitions and cooperation are key topics in multi-agent systems (mas). They enable agents to achieve goals that they may not have been able to achieve independently. A range of previous studies have found that many problems in coalitional games tend to be computationally intractable - that is, the computational complexity grows rapidly as a function of the number of participating agents. However, these hardness results generally require that each agent is of a different type. Here, we observe that in many mas settings, while the number of agents may grow, the number of different types of agents remains small. We formally define the notion of agent types in cooperative games. We then re-examine the computational complexity of the different coalition formation problems when assuming that the number of agent types is fixed. We show that most of the previously hard problems become polynomial when the number of agent types is fixed. We consider multiple different game formulations and representations (characteristic function with subadditive utilities, crg, and graphical representations) and several different computational problems (including stability, core-emptiness, and Shapley value).
    9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2010), Toronto, Canada, May 10-14, 2010, Volume 1-3; 01/2010
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    Yonatan Aumann, Yair Dombb
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    ABSTRACT: We analyze the Pareto efficiency, or inefficiency, of solutions to routing games and load balancing games, focusing on Nash equilibria and greedy solutions to these games. For some settings, we show that the solutions are necessarily Pareto optimal. When this is not the case, we provide a measure to quantify the distance of the solution from Pareto efficiency. Using this measure, we provide upper and lower bounds on the “Pareto inefficiency” of the different solutions. The settings we consider include load balancing games on identical, uniformly-related, and unrelated machines, both using pure and mixed strategies, and nonatomic routing in general and some specific networks.
    Algorithmic Game Theory - Third International Symposium, SAGT 2010, Athens, Greece, October 18-20, 2010. Proceedings; 01/2010
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    ABSTRACT: Recently, a new pattern matching paradigm was proposed, pattern matching with address errors. In this paradigm approximate string matching problems are studied, where the content is unaltered and only the locations of the different entries may change. Specifically, a broad class of problems was defined-the class of rearrangement errors. In this type of error the pattern is transformed through a sequence of rearrangement operations, each with an associated cost. The natural @?"1 and @?"2 rearrangement systems were considered. The best algorithm presented for general patterns, that may have repeating symbols, is O(nm). In this paper, we show that the problem can be approximated in linear time for general patterns! Another natural rearrangement system is considered in this paper-the @?"~ rearrangement distance. For this new rearrangement system efficient exact solutions for different variants of the problem are provided, as well as a faster approximation.
    Theoretical Computer Science 10/2009; 410(43):4382-4390. · 0.49 Impact Factor
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    ABSTRACT: Historically, approximate pattern matching has mainly focused at coping with errors in the data, while the order of the text/pattern was assumed to be more or less correct. In this paper we consider a class of pattern matching problems where the content is assumed to be correct, while the locations may have shifted/changed. We formally define a broad class of problems of this type, capturing situations in which the pattern is obtained from the text by a sequence of rearrangements. We consider several natural rearrangement schemes, including the analogues of the ℓ1 and ℓ2 distances, as well as two distances based on interchanges. For these, we present efficient algorithms to solve the resulting string matching problems.
    Journal of Computer and System Sciences 09/2009; · 1.00 Impact Factor
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    Theor. Comput. Sci. 01/2009; 410:5334-5346.
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    J. Comput. Syst. Sci. 01/2009; 75:359-370.
  • Theor. Comput. Sci. 01/2009; 410:4382-4390.
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    Noam Hazon, Yonatan Aumann, Sarit Kraus
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    ABSTRACT: This paper considers the setting wherein a group of agents (e.g., robots) is seeking to obtain a given tan- gible good, potentially available at different loca- tions in a physical environment. Traveling between locations, as well as acquiring the good at any given location consumes from the resources available to the agents (e.g., battery charge). The availability of the good at any given location, as well as the ex- act cost of acquiring the good at the location is not fully known in advance, and observed only upon physically arriving at the location. However, a- priori probabilities on the availability and poten- tial cost are provided. Given such as setting, the problem is to find a strategy/plan that maximizes the probability of acquiring the good while mini- mizing resource consumption. Sample applications include agents in exploration and patrol missions, e.g., rovers on Mars seeking to mine a specific min- eral. Although this model captures many real world scenarios, it has not been investigated so far. We focus on the case where locations are aligned along a path, and study several variants of the prob- lem, analyzing the effects of communication and coordination. For the case that agents can com- municate, we present a polynomial algorithm that works for any fixed number of agents. For non- communicating agents, we present a polynomial al- gorithm that is suitable for any number of agents. Finally, we analyze the difference between homo- geneous and heterogeneous agents, both with re- spect to their allotted resources and with respect to their capabilities.
    IJCAI 2009, Proceedings of the 21st International Joint Conference on Artificial Intelligence, Pasadena, California, USA, July 11-17, 2009; 01/2009
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    ABSTRACT: In this paper, the optimality proof of Lempel-Ziv coding is re-studied, and a much more general compression optimality theorem is derived. In particular, the property of quasi-distinct parsing is defined. This property is much weaker than distinct parsing required in the original proof, yet we show that the theorem holds with this weaker property as well. This provides a better understanding of the optimality proof of Lempel-Ziv coding, together with a new tool for proving optimality of other compression schemes. To demonstrate the possible use of this generalization, a new coding method – the APT coding – is presented. This new coding method is based on a principle that is very different from Lempel-Ziv’s coding. Moreover, it does not directly define any parsing technique. Nevertheless, APT coding is analyzed in this paper and using the generalized theorem shown to be asymptotically optimal up to a constant factor, if APT quasi-distinctness hypothesis holds. An empirical evidence that this hypothesis holds is also given.
    Combinatorial Pattern Matching, 20th Annual Symposium, CPM 2009, Lille, France, June 22-24, 2009, Proceedings; 01/2009

Publication Stats

1k Citations
31.89 Total Impact Points

Institutions

  • 1970–2014
    • Bar Ilan University
      • Department of Computer Science
      Gan, Tel Aviv, Israel
  • 2006–2007
    • Technion - Israel Institute of Technology
      H̱efa, Haifa District, Israel
  • 2003
    • CUNY Graduate Center
      New York City, New York, United States
  • 1990–1994
    • Hebrew University of Jerusalem
      • • Otto Loewi Minerva Center for Neurobiology
      • • Rachel and Selim Benin School of Computer Science and Engineering
      Yerushalayim, Jerusalem District, Israel
  • 1993
    • Weizmann Institute of Science
      Israel