422,378 research outputs found
On Conceptually Simple Algorithms for Variants of Online Bipartite Matching
We present a series of results regarding conceptually simple algorithms for
bipartite matching in various online and related models. We first consider a
deterministic adversarial model. The best approximation ratio possible for a
one-pass deterministic online algorithm is , which is achieved by any
greedy algorithm. D\"urr et al. recently presented a -pass algorithm called
Category-Advice that achieves approximation ratio . We extend their
algorithm to multiple passes. We prove the exact approximation ratio for the
-pass Category-Advice algorithm for all , and show that the
approximation ratio converges to the inverse of the golden ratio
as goes to infinity. The convergence is
extremely fast --- the -pass Category-Advice algorithm is already within
of the inverse of the golden ratio.
We then consider a natural greedy algorithm in the online stochastic IID
model---MinDegree. This algorithm is an online version of a well-known and
extensively studied offline algorithm MinGreedy. We show that MinDegree cannot
achieve an approximation ratio better than , which is guaranteed by any
consistent greedy algorithm in the known IID model.
Finally, following the work in Besser and Poloczek, we depart from an
adversarial or stochastic ordering and investigate a natural randomized
algorithm (MinRanking) in the priority model. Although the priority model
allows the algorithm to choose the input ordering in a general but well defined
way, this natural algorithm cannot obtain the approximation of the Ranking
algorithm in the ROM model
Pruning Error Minimization in Least Squares Support Vector Machines
The support vector machine (SVM) is a method for classification and for function approximation. This method commonly makes use of an /spl epsi/-insensitive cost function, meaning that errors smaller than /spl epsi/ remain unpunished. As an alternative, a least squares support vector machine (LSSVM) uses a quadratic cost function. When the LSSVM method is used for function approximation, a nonsparse solution is obtained. The sparseness is imposed by pruning, i.e., recursively solving the approximation problem and subsequently omitting data that has a small error in the previous pass. However, omitting data with a small approximation error in the previous pass does not reliably predict what the error will be after the sample has been omitted. In this paper, a procedure is introduced that selects from a data set the training sample that will introduce the smallest approximation error when it will be omitted. It is shown that this pruning scheme outperforms the standard one
Small Space Stream Summary for Matroid Center
In the matroid center problem, which generalizes the k-center problem, we need to pick a set of centers that is an independent set of a matroid with rank r. We study this problem in streaming, where elements of the ground set arrive in the stream. We first show that any randomized one-pass streaming algorithm that computes a better than Delta-approximation for partition-matroid center must use Omega(r^2) bits of space, where Delta is the aspect ratio of the metric and can be arbitrarily large. This shows a quadratic separation between matroid center and k-center, for which the Doubling algorithm [Charikar et al., 1997] gives an 8-approximation using O(k)-space and one pass. To complement this, we give a one-pass algorithm for matroid center that stores at most O(r^2 log(1/epsilon)/epsilon) points (viz., stream summary) among which a (7+epsilon)-approximate solution exists, which can be found by brute force, or a (17+epsilon)-approximation can be found with an efficient algorithm. If we are allowed a second pass, we can compute a (3+epsilon)-approximation efficiently.
We also consider the problem of matroid center with z outliers and give a one-pass algorithm that outputs a set of O((r^2+rz)log(1/epsilon)/epsilon) points that contains a (15+epsilon)-approximate solution. Our techniques extend to knapsack center and knapsack center with z outliers in a straightforward way, and we get algorithms that use space linear in the size of a largest feasible set (as opposed to quadratic space for matroid center)
Pass-Through And The Prediction Of Merger Price Effects
We use Monte Carlo experiments to study how pass-through can improve merger price predictions, focusing on the first order approximation (FOA) proposed in Jaffe and Weyl [2013]. FOA addresses the functional form misspecification that can exist in standard merger simulations. We find that the predictions of FOA are tightly distributed around the true price effects if pass-through is precise, but that measurement error in pass-through diminishes accuracy. As a comparison to FOA, we also study a methodology that uses pass-through to select among functional forms for use in simulation. This alternative also increases accuracy relative to standard merger simulation and proves more robust to measurement error
Maximum Matching in Turnstile Streams
We consider the unweighted bipartite maximum matching problem in the one-pass
turnstile streaming model where the input stream consists of edge insertions
and deletions. In the insertion-only model, a one-pass -approximation
streaming algorithm can be easily obtained with space , where
denotes the number of vertices of the input graph. We show that no such result
is possible if edge deletions are allowed, even if space is
granted, for every . Specifically, for every , we show that in the one-pass turnstile streaming model, in order to compute
a -approximation, space is
required for constant error randomized algorithms, and, up to logarithmic
factors, space is sufficient. Our lower bound result is
proved in the simultaneous message model of communication and may be of
independent interest
Network Utility Maximization under Maximum Delay Constraints and Throughput Requirements
We consider the problem of maximizing aggregate user utilities over a
multi-hop network, subject to link capacity constraints, maximum end-to-end
delay constraints, and user throughput requirements. A user's utility is a
concave function of the achieved throughput or the experienced maximum delay.
The problem is important for supporting real-time multimedia traffic, and is
uniquely challenging due to the need of simultaneously considering maximum
delay constraints and throughput requirements. We first show that it is
NP-complete either (i) to construct a feasible solution strictly meeting all
constraints, or (ii) to obtain an optimal solution after we relax maximum delay
constraints or throughput requirements up to constant ratios. We then develop a
polynomial-time approximation algorithm named PASS. The design of PASS
leverages a novel understanding between non-convex maximum-delay-aware problems
and their convex average-delay-aware counterparts, which can be of independent
interest and suggest a new avenue for solving maximum-delay-aware network
optimization problems. Under realistic conditions, PASS achieves constant or
problem-dependent approximation ratios, at the cost of violating maximum delay
constraints or throughput requirements by up to constant or problem-dependent
ratios. PASS is practically useful since the conditions for PASS are satisfied
in many popular application scenarios. We empirically evaluate PASS using
extensive simulations of supporting video-conferencing traffic across Amazon
EC2 datacenters. Compared to existing algorithms and a conceivable baseline,
PASS obtains up to improvement of utilities, by meeting the throughput
requirements but relaxing the maximum delay constraints that are acceptable for
practical video conferencing applications
Compositional synthesis of discrete event systems via synthesis equivalence
A two-pass algorithm for compositional synthesis of modular supervisors for largescale systems of composed finite-state automata is proposed. The first pass provides an efficient method to determine whether a supervisory control problem has a solution, without explicitly constructing the synchronous composition of all components. If a solution exists, the second pass yields an over-approximation of the least restrictive solution which, if nonblocking, is a modular representation of the least restrictive supervisor. Using a new type of equivalence of nondeterministic processes, called synthesis equivalence, a wide range of abstractions can be employed to mitigate state-space explosion throughout the algorithm
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