arXiv subjects

Yannai A. Gonczarowski

Publications and source records attributed to Yannai A. Gonczarowski.

42 records · Page 3Linked to original sources

arXiv2014

Manipulation of Stable Matchings using Minimal Blacklists

Gale and Sotomayor (1985) have shown that in the Gale-Shapley matching algorithm (1962), the proposed-to side W (referred to as women there) can strategically force the W-optimal stable matching as the M-optimal one by truncating their preference lists, each woman possibly blacklisting all but one man. As Gusfield and Irving have already noted in 1989, no results are known regarding achieving this feat by means other than such preference-list truncation, i.e. by also permuting preference lists. We answer Gusfield and Irving's open question by providing tight upper bounds on the amount of blacklists and their combined size, that are required by the women to force a given matching as the M-optimal stable matching, or, more generally, as the unique stable matching. Our results show that the coalition of all women can strategically force any matching as the unique stable matching, using preference lists in which at most half of the women have nonempty blacklists, and in which the average blacklist size is less than 1. This allows the women to manipulate the market in a manner that is far more inconspicuous, in a sense, than previously realized. When there are less women than men, we show that in the absence of blacklists for men, the women can force any matching as the unique stable matching without blacklisting anyone, while when there are more women than men, each to-be-unmatched woman may have to blacklist as many as all men. Together, these results shed light on the question of how much, if at all, do given preferences for one side a priori impose limitations on the set of stable matchings under various conditions. All of the results in this paper are constructive, providing efficient algorithms for calculating the desired strategies.

cs.GT↗

arXiv2013

Good, Better, Best! - Unbeatable Protocols for Consensus and Set Consensus

While the very first consensus protocols for the synchronous model were designed to match the worst-case lower bound, deciding in exactly t+1 rounds in all runs, it was soon realized that they could be strictly improved upon by early stopping protocols. These dominate the first ones, by always deciding in at most t+1 rounds, but often much faster. A protocol is unbeatable if it can't be strictly dominated. Unbeatability is often a much more suitable notion of optimality for distributed protocols than worst-case performance. Using a knowledge-based analysis, this paper studies unbeatability for both consensus and k-set consensus. We present unbeatable solutions to non-uniform consensus and k-set consensus, and uniform consensus in synchronous message-passing contexts with crash failures. The k-set consensus problem is much more technically challenging than consensus, and its analysis has triggered the development of the topological approach to distributed computing. Worst-case lower bounds for this problem have required either techniques based on algebraic topology, or reduction-based proofs. Our proof of unbeatability is purely combinatorial, and is a direct, albeit nontrivial, generalization of the one for consensus. We also present an alternative topological unbeatability proof that allows to understand the connection between the connectivity of protocol complexes and the decision time of processes. For the synchronous model, only solutions to the uniform variant of k-set consensus have been offered. Based on our unbeatable protocols for uniform consensus and for non-uniform k-set consensus, we present a uniform k-set consensus protocol that strictly dominates all known solutions to this problem in the synchronous model.

cs.DC↗

arXiv2013

Timely Common Knowledge

Coordinating activities at different sites of a multi-agent system typically imposes epistemic constraints on the participants. Specifying explicit bounds on the relative times at which actions are performed induces combined temporal and epistemic constraints on when agents can perform their actions. This paper characterises the interactive epistemic state that arises when actions must meet particular temporal constraints. The new state, called timely common knowledge, generalizes common knowledge, as well as other variants of common knowledge. While known variants of common knowledge are defined in terms of a fixed point of an epistemic formula, timely common knowledge is defined in terms of a vectorial fixed point of temporal-epistemic formulae. A general class of coordination tasks with timing constraints is defined, and timely common knowledge is used to characterise both solvability and optimal solutions of such tasks. Moreover, it is shown that under natural conditions, timely common knowledge is equivalent to an infinite conjunction of temporal-epistemic formulae, in analogy to the popular definition of common knowledge.

cs.LO↗

arXiv2013

Satisfiability and Canonisation of Timely Constraints

We abstractly formulate an analytic problem that arises naturally in the study of coordination in multi-agent systems. Let I be a set of arbitrary cardinality (the set of actions) and assume that for each pair of distinct actions (i,j), we are given a number δ(i,j). We say that a function t, specifying a time for each action, satisfies the timely constraint δ if for every pair of distinct actions (i,j), we have t(j)-t(i) <= δ(i,j) (and thus also t(j)-t(i) >= -δ(j,i)). While the approach that first comes to mind for analysing these definitions is an analytic/geometric one, it turns out that graph-theoretic tools yield powerful results when applied to these definitions. Using such tools, we characterise the set of satisfiable timely constraints, and reduce the problem of satisfiability of a timely constraint to the all-pairs shortest-path problem, and for finite I, furthermore to the negative-cycle detection problem. Moreover, we constructively show that every satisfiable timely constraint has a minimal satisfying function - a key milestone on the way to optimally solving a large class of coordination problems - and reduce the problem of finding this minimal satisfying function, as well as the problems of classifying and comparing timely constraints, to the all-pairs shortest-path problem. At the heart of our analysis lies the constructive definition of a "nicely-behaved" representative for each class of timely constraints sharing the same set of satisfying functions. We show that this canonical representative, as well as the map from such canonical representatives to the the sets of functions satisfying the classes of timely constraints they represent, has many desired properties, which provide deep insights into the structure underlying the above definitions.

math.CO↗

arXiv2012

Timely Coordination in a Multi-Agent System

In a distributed algorithm, multiple processes, or agents, work toward a common goal. More often than not, the actions of some agents are dependent on the previous execution (if not also on the outcome) of the actions of other agents. The resulting interdependencies between the timings of the actions of the various agents give rise to the study of methods for timely coordination of these actions. In this work, we formulate and mathematically analyze "Timely-Coordinated Response" - a novel multi-agent coordination problem in which the time difference between each pair of actions may be constrained by upper and/or lower bounds. This problem generalizes coordination problems previously studied by Halpern and Moses and by Ben-Zvi and Moses. We optimally solve timely-coordinated response in two ways: using a generalization of the fixed-point approach of Halpern and Moses, and using a generalization of the "syncausality" approach of Ben-Zvi and Moses. We constructively show the equivalence of the solutions yielded by both approaches, and by combining them, derive strengthened versions of known results for some previously-defined special cases of this problem. Our analysis is conducted under minimal assumptions: we work in a continuous-time model with possibly infinitely many agents. The general results we obtain for this model reduce to stronger ones for discrete-time models with only finitely many agents. In order to distill the properties of such models that are significant to this reduction, we define several classes of naturally-occurring models, which in a sense separate the different results. We present both a more practical optimal solution, as well as a surprisingly simple condition for solvability, for timely coordinated response under these models. Finally, we show how our results generalize the results known for previously-studied special cases of this problem.

cs.MA↗

arXiv2011

On Sisterhood in the Gale-Shapley Matching Algorithm

Lying in order to manipulate the Gale-Shapley matching algorithm has been studied by Dubins and Friedman and by Gale and Sotomayor and was shown to be generally more appealing to the proposed-to side (denoted as the women in Gale and Shapley's original paper) than to the proposing side (denoted as men there). It can also be shown that in the case of lying women, for every woman who is better-off due to lying, there exists a man who is worse-off. In this paper, we show that an even stronger dichotomy between the goals of the sexes holds, namely, if no woman is worse-off then no man is better-off, while a form of sisterhood between the lying and the "innocent" women also holds, namely, if none of the former are worse-off, then neither is any of the latter. This paper is based upon an undergraduate ("Amirim") thesis of the first author.

cs.GT↗