We investigate the parameters in terms of which the complexity of sublinear-time algorithms should be expressed. Our goal is to find input parameters that are tailored to the combinatorics of the specific problem bein...
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We investigate the parameters in terms of which the complexity of sublinear-time algorithms should be expressed. Our goal is to find input parameters that are tailored to the combinatorics of the specific problem being studied and design algorithms that run faster when these parameters are small. This direction enables us to surpass the (worst-case) lower bounds, expressed in terms of the input size, for several problems. Our aim is to develop a similar level of understanding of the complexity of sublinear-time algorithms to the one that was enabled by research in parameterized complexity for classical algorithms. Specifically, we focus on testing properties of functions. By parameterizing the query complexity in terms of the size r of the image of the input function, we obtain testers for monotonicity and convexity of functions of the form f : [n] -> R with query complexity O(log r), with no dependence on n. The result for monotonicity circumvents the Omega(logn) lower bound by Fischer (Inf. Comput. 2004) for this problem. We present several other parameterized testers, providing compelling evidence that expressing the query complexity of property testers in terms of the input size is not always the best choice.
We investigate a new class of geometric problems based on the idea of online error correction. Suppose one is given access to a large geometric dataset though a query mechanism;for example, the dataset could be a terr...
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We investigate a new class of geometric problems based on the idea of online error correction. Suppose one is given access to a large geometric dataset though a query mechanism;for example, the dataset could be a terrain and a query might ask for the coordinates of a particular vertex or for the edges incident to it. Suppose, in addition, that the dataset satisfies some known structural property P (for example, monotonicity or convexity) but that, because of errors and noise, the queries occasionally provide answers that violate P. Can one design a filter that modifies the query's answers so that (i) the output satisfies P;(ii) the amount of data modification is minimized? We provide upper and lower bounds on the complexity of online reconstruction for convexity in 2D and 3D.
We consider distributed elections, where there is a center and k sites. In such distributed elections, each voter has preferences over some set of candidates, and each voter is assigned to exactly one site such that e...
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ISBN:
(纸本)9781510855076
We consider distributed elections, where there is a center and k sites. In such distributed elections, each voter has preferences over some set of candidates, and each voter is assigned to exactly one site such that each site is aware only of the voters assigned to it. The center is able to directly communicate with each of the sites. We are interested in designing communication-efficient protocols, allowing the center to maintain (i.e., declare) a candidate which, with arbitrary high probability, is guaranteed to be a winner, or at least close to being a winner. We consider various single-winner voting rules, such as variants of Approval voting and scoring rules, tournament-based voting rules, and several round-based voting rules For these voting rules, we show that, using communication which is logarithmic in the number of voters, it is possible for the center to maintain such approximate winners. We complement our protocols with lower bounds. Our results have implications in various scenarios, such as aggregating customer preferences in online shopping websites or supermarket chains and collecting votes from different polling stations of political elections.
In hedonic games, players form coalitions based on individual preferences over the group of players they belong to. Several concepts to describe the stability of coalition structures in a game have been proposed and a...
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ISBN:
(纸本)9781450363099
In hedonic games, players form coalitions based on individual preferences over the group of players they belong to. Several concepts to describe the stability of coalition structures in a game have been proposed and analysed. However, prior research focuses on algorithms with time complexity that is at least linear in the input size. In the light of very large games that arise from, e.g., social networks and advertising, we initiate the study of sublinear time property testing algorithms for existence and verification problems under several notions of coalition stability in a model of hedonic games represented by graphs with bounded degree. In graph property testing, one shall decide whether a given input has a property (e.g., a game admits a stable coalition structure) or is far from it, i.e., one has to modify at least an ε-fraction of the input (e.g., the game's preferences) to make it have the property. In particular, we consider verification of perfection, individual rationality, Nash stability, and (contractual) individual stability. Furthermore, we show that while there is always a Nash-stable coalition (which also implies individually stable coalitions), the existence of a perfect coalition can be tested. All our testers have one-sided error and time complexity that is independent of the input size.
The standard definition of property testing endows the tester with the ability to make arbitrary queries to "elements" of the tested object. In contrast, sample-based testers only obtain independently distri...
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ISBN:
(纸本)9781450333337
The standard definition of property testing endows the tester with the ability to make arbitrary queries to "elements" of the tested object. In contrast, sample-based testers only obtain independently distributed elements (a.k.a. labeled samples) of the tested object. While sample-based testers were defined by Goldreich, Goldwasser, and Ron JACM 1998), with few exceptions, most research in property testing is focused on query-based testers. In this work, we advance the study of sample-based property testers by providing several general positive results as well as by revealing relations between variants of this testing model. In particular: We show that certain types of query-based testers yield sample-based testers of sublinear sample complexity. For example, this holds for a natural class of proximity oblivious *** study the relation between distribution-free sample-based testers and one-sided error sample-based testers w.r.t. the uniform *** most of this work ignores the time complexity of testing, one part of it does focus on this aspect. The main result in this part is a sublinear-time sample-based tester in the dense graphs model for k-Colorability, for any k > 2.
We consider elections where the voters come one at a time, in a streaming fashion, and devise space-efficient algorithms which identify an approximate winning committee with respect to common multiwinner proportional ...
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ISBN:
(纸本)9781510855076
We consider elections where the voters come one at a time, in a streaming fashion, and devise space-efficient algorithms which identify an approximate winning committee with respect to common multiwinner proportional representation voting rules; specifically, we consider the Approval-based and the Borda-based variants of both the Chamberlin-Courant rule and the Monroe rule. We complement our algorithms with lower bounds. Somewhat surprisingly, our results imply that, using space which does not depend on the number of voters it is possible to efficiently identify an approximate representative committee of fixed size over vote streams with huge number of voters.
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