Roee Engelberg
PhD in Computer Science, Technion.
Authored Publications
Google Publications
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Covering Uncommon Ground: Followup Question Generation for Answer Assessment
Alexandre Djerbetian
Reut Tsarfaty
Amir Globerson
ACL(2023) (to appear)
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In educational dialogue settings students often provide answers that are incomplete. In other words, there is a gap between the answer the student provides and the perfect answer expected by the teacher. Successful dialogue hinges on the teacher asking about this gap in an effective manner, thus creating a rich and interactive educational experience. Here we focus on the problem of generating such gap-focused questions (GFQ) automatically. We define the task, highlight key desired aspects of a good GFQ, and propose a model that satisfies these. Finally, we provide an evaluation of our generated questions and compare them to manually generated ones, demonstrating competitive performance.
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In many computational and economic models of multi-agent interaction, each participant repeatedly "best-responds" to the others' actions. Game theory research on the prominent "best-response dynamics" model typically relies on the premise that the interaction between agents is somehow synchronized. However, in many real-life settings, e.g., internet protocols and large-scale markets, the interaction between participants is asynchronous. We tackle the following important questions: (1) When are best-response dynamics guaranteed to converge to an equilibrium even under asynchrony? (2) What is the (computational and communication) complexity of verifying guaranteed convergence? We show that, in general, verifying guaranteed convergence is intractable. In fact, our main negative result establishes that this task is undecidable. We exhibit, in contrast, positive results for several environments of interest, including complete, computationally-tractable, characterizations of convergent systems. We discuss the algorithmic implications of our results, which extend beyond best-response dynamics to applications such as asynchronous Boolean circuits.
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Equilibria in Online Games
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We initiate the study of scenarios that combine online decision making with interaction between noncooperative agents. To this end we introduce online games that model such scenarios as noncooperative games, and lay the foundations for studying this model. Roughly speaking, an online game captures systems in which independent agents serve requests in a common environment. The requests arrive in an online fashion, and each is designated to be served by a different agent. The cost incurred by serving a request is paid by the serving agent, and naturally the agents seek to minimize the total cost to themselves. Since the agents are independent, it is unlikely that some central authority can enforce a policy or an algorithm (centralized or distributed) on them, and thus, the agents can be viewed as selfish players in a noncooperative game. In this game, the players have to choose as a strategy an online algorithm according to which requests are served. To further facilitate the game-theoretic approach, we suggest the measure of competitive analysis as the players' decision criterion. As the expected result of noncooperative games is an equilibrium, the question of finding the equilibria of a game is of central importance, and thus it is the central issue on which we concentrate in this paper. We study some natural examples for online games; in order to obtain general insights and develop generic techniques, we present an abstract model for the study of online games generalizing metrical task systems. We suggest a method for constructing equilibria in this model and further devise techniques for implementing it.
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Weakly-Acyclic (Internet) Routing Games
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Weakly-acyclic games—a superclass of potential games—capture distributed environments where simple, globally-asynchronous interactions between strategic agents are guaranteed to converge to an equilibrium. We explore the class of routing games introduced in Fabrikant and Papadimitriou (The Complexity of Game Dynamics: BGP Oscillations, Sink Equilibria, and Beyond, pp. 844–853, 2008) and in Levin et al. (Interdomain Routing and Games, pp. 57–66, 2008), which models important aspects of routing on the Internet. We show that, in interesting contexts, such routing games are weakly acyclic and, moreover, that pure Nash equilibria in such games can be found in a computationally efficient manner.
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Improved Approximation Algorithms for the Spanning Star Forest Problem
Ning Chen
C. Thach Nguyen
Prasad Raghavendra
Atri Rudra
Gyanit Singh
Algorithmica, 65(3)(2013), pp. 498-516
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A star graph is a tree of diameter at most two. A star forest is a graph that consists of node-disjoint star graphs. In the spanning star forest problem, given an unweighted graph G, the objective is to find a star forest that contains all vertices of G and has the maximum number of edges. This problem is the complement of the dominating set problem in the following sense: On a graph with n vertices, the size of the maximum spanning star forest is equal to n minus the size of the minimum dominating set.
We present a 0.71-approximation algorithm for this problem, improving upon the approximation factor of 0.6 of Nguyen et al. (SIAM J. Comput. 38:946–962, 2008). We also present a 0.64-approximation algorithm for the problem on node-weighted graphs. Finally, we present improved hardness of approximation results for the weighted (both edge-weighted and node-weighted) versions of the problem.
Our algorithms use a non-linear rounding scheme, which might be of independent interest.
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Cut Problems in Graphs with a Budget Constraint. Journal of Discrete Algorithms
Jochen Könemann
Stefano Leonardi
Joseph (Seffi) Naor
J. Discrete Algorithms, 5(2)(2007), pp. 262-279
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We study budgeted variants of classical cut problems: the Multiway Cut problem, the Multicut problem, and the k-Cut problem, and provide approximation algorithms for these problems. Specifically, for the budgeted multiway cut and the k-cut problems we provide constant factor approximation algorithms. We show that the budgeted multicut problem is at least as hard to approximate as the sparsest cut problem, and we provide a bi-criteria approximation algorithm for it.
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