79 research outputs found
Approximation algorithms for distributed and selfish agents
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.Includes bibliographical references (p. 157-165).Many real-world systems involve distributed and selfish agents who optimize their own objective function. In these systems, we need to design efficient mechanisms so that system-wide objective is optimized despite agents acting in their own self interest. In this thesis, we develop approximation algorithms and decentralized mechanisms for various combinatorial optimization problems in such systems. First, we investigate the distributed caching and a general set of assignment problems. We develop an almost tight LP-based ... approximation algorithm and a local search ... approximation algorithm for these problems. We also design efficient decentralized mechanisms for these problems and study the convergence of the corresponding games. In the following chapters, we study the speed of convergence to high quality solutions on (random) best-response paths of players. First, we study the average social value on best response paths in basic-utility, market sharing, and cut games. Then, we introduce the sink equilibrium as a new equilibrium concept. We argue that, unlike Nash equilibria, the selfish behavior of players converges to sink equilibria and all strategic games have a sink equilibrium. To illustrate the use of this new concept, we study the social value of sink equilibria in weighted selfish routing (or weighted congestion) games and valid-utility (or submodular-utility) games. In these games, we bound the average social value on random best-response paths for sink equilibria.. Finally, we study cross-monotonic cost sharings and group-strategyproof mechanisms.(cont.) We study the limitations imposed by the cross-monotonicity property on cost-sharing schemes for several combinatorial optimization games including set cover and metric facility location. We develop a novel technique based on the probabilistic method for proving upper bounds on the budget-balance factor of cross-monotonic cost sharing schemes, deriving tight or nearly-tight bounds for these games. At the end, we extend some of these results to group-strategyproof mechanisms.by Vahab S. Mirrokni.Ph.D
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Diversity Maximization Under Matroid Constraints
Aggregator websites typically present documents in the form of representative clusters. In order for users to get a broader perspective,it is important to deliver a diversified set of representative documents in those clusters. One approach to diversification is to maximize the average dissimilarity among documents. Another way to capture diversity is to avoid showing several documents from the same category (e.g. from the same news channel). We model the latter approach as a (partition) matroid constraint, and study diversity maximization problems under matroid constraints. We present the first constant-factor approximation algorithm for this problem,using a new technique. Our local search 0:5-approximation algorithm is also the first constant-factor approximation for the maxdispersion problem under matroid constraints. Our combinatorial proof technique for maximizing diversity under matroid constraints uses the existence of a family of Latin squares which may also be of independent interest. In order to apply these diversity maximization algorithms in the context of aggregator websites and as a preprocessing step for our diversity maximization tool, we develop greedy clustering algorithms that maximize weighted coverage of a predefined set of topics. Our algorithms are based on computing a set of cluster centers, where clusters are formed around them. We show the better performance of our algorithms for diversity and coverage maximization by running experiments on real (Twitter) and synthetic data in the context of real-time search over micro-posts. Finally we perform a user study validating our algorithms and diversity metrics
Dynamic Algorithms for the Massively Parallel Computation Model
The Massive Parallel Computing (MPC) model gained popularity during the last
decade and it is now seen as the standard model for processing large scale
data. One significant shortcoming of the model is that it assumes to work on
static datasets while, in practice, real-world datasets evolve continuously. To
overcome this issue, in this paper we initiate the study of dynamic algorithms
in the MPC model.
We first discuss the main requirements for a dynamic parallel model and we
show how to adapt the classic MPC model to capture them. Then we analyze the
connection between classic dynamic algorithms and dynamic algorithms in the MPC
model. Finally, we provide new efficient dynamic MPC algorithms for a variety
of fundamental graph problems, including connectivity, minimum spanning tree
and matching.Comment: Accepted to the 31st ACM Symposium on Parallelism in Algorithms and
Architectures (SPAA 2019
Bid Optimization in Broad-Match Ad auctions
Ad auctions in sponsored search support ``broad match'' that allows an
advertiser to target a large number of queries while bidding only on a limited
number. While giving more expressiveness to advertisers, this feature makes it
challenging to optimize bids to maximize their returns: choosing to bid on a
query as a broad match because it provides high profit results in one bidding
for related queries which may yield low or even negative profits.
We abstract and study the complexity of the {\em bid optimization problem}
which is to determine an advertiser's bids on a subset of keywords (possibly
using broad match) so that her profit is maximized. In the query language model
when the advertiser is allowed to bid on all queries as broad match, we present
an linear programming (LP)-based polynomial-time algorithm that gets the
optimal profit. In the model in which an advertiser can only bid on keywords,
ie., a subset of keywords as an exact or broad match, we show that this problem
is not approximable within any reasonable approximation factor unless P=NP. To
deal with this hardness result, we present a constant-factor approximation when
the optimal profit significantly exceeds the cost. This algorithm is based on
rounding a natural LP formulation of the problem. Finally, we study a budgeted
variant of the problem, and show that in the query language model, one can find
two budget constrained ad campaigns in polynomial time that implement the
optimal bidding strategy. Our results are the first to address bid optimization
under the broad match feature which is common in ad auctions.Comment: World Wide Web Conference (WWW09), 10 pages, 2 figure
Feature Cross Search via Submodular Optimization
In this paper, we study feature cross search as a fundamental primitive in
feature engineering. The importance of feature cross search especially for the
linear model has been known for a while, with well-known textbook examples. In
this problem, the goal is to select a small subset of features, combine them to
form a new feature (called the crossed feature) by considering their Cartesian
product, and find feature crosses to learn an \emph{accurate} model. In
particular, we study the problem of maximizing a normalized Area Under the
Curve (AUC) of the linear model trained on the crossed feature column.
First, we show that it is not possible to provide an -approximation algorithm for this problem unless the exponential time
hypothesis fails. This result also rules out the possibility of solving this
problem in polynomial time unless . On the positive
side, by assuming the \naive\ assumption, we show that there exists a simple
greedy -approximation algorithm for this problem. This result is
established by relating the AUC to the total variation of the commutator of two
probability measures and showing that the total variation of the commutator is
monotone and submodular. To show this, we relate the submodularity of this
function to the positive semi-definiteness of a corresponding kernel matrix.
Then, we use Bochner's theorem to prove the positive semi-definiteness by
showing that its inverse Fourier transform is non-negative everywhere. Our
techniques and structural results might be of independent interest.Comment: Accepted to ESA 2021. Authors are ordered alphabeticall
On the inventory cycle and the instability of the competitive mechanism
This paper presents a model of the business cycle with perfect foresight where the mere presence of inventories is responsible for the appearance of the cycle. The basic assumption of the model is that the price system does not adjust instantaneously to its competitive value. Then inventory holding destabilizes the tâtonnement dynamics and creates the cycle. A Wicksellian cumulative process generates both the booms, where the real rate of return on cash is smaller than the natural rate of interest obtained by the inventory holders, and the recessions, where inventories are dominated by money balances
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