3276234
Minimizing average flow time on related machines
We give the first on-line poly-logarithmic competitve algorithm for minimizing average flow time with preemption on related machines, i.e., when machines can have different speeds. This also yields the first poly-logarithmic polynomial time approximation algorithm for this problem.More specifically, we give an O(log2 P • log S)-competitive algorithm, where P is the ratio of the biggest and the smallest processing time of a job, and S is the ratio of the highest and the smallest speed of a machine. Our algorithm also has the nice property that it is non-migratory. The scheduling algorithm is based on the concept of making jobs wait for a long enough time before scheduling them on slow machines.
995281
Deterministic wavelet thresholding for maximum-error metrics
Several studies have demonstrated the effectiveness of the wavelet, decomposition as a tool for reducing large amounts of data down to compact, wavelet synopses that can be used to obtain fast, accurate approximate answers to user queries. While conventional wavelet synopses are based on greedily minimizing the overall root-mean-squared (i.e., L2-norm) error in the data approximation, recent work has demonstrated that such synopses can suffer from important problems, including severe bias and wide variance in the quality of the data reconstruction, and lack of non-trivial guarantees for individual approximate answers. As a result, probabilistic thresholding schemes have been recently proposed as a means of building wavelet synopses that try to probabilistically control other approximation-error metrics, such as the maximum relative error in data-value reconstruction, which is arguably the most important for approximate query answers and meaningful error guarantees.One of the main open problems posed by this earlier work is whether it is possible to design efficient deterministic wavelet-thresholding algorithms for minimizing non-L2 error metrics that are relevant to approximate query processing systems, such as maximum relative or maximum absolute error. Obviously, such algorithms can guarantee better wavelet synopses and avoid the pitfalls of probabilistic techniques (e.g., "bad" coin-flip sequences) leading to poor solutions. In this paper, we address this problem and propose novel, computationally efficient schemes for deterministic wavelet thresholding with the objective of optimizing maximum-error metrics. We introduce an optimal low polynomial-time algorithm for one-dimensional wavelet thresholding--our algorithm is based on a new Dynamic-Programming (DP) formulation, and can be employed to minimize the maximum relative or absolute error in the data reconstruction. Unfortunately, directly extending our one-dimensional DP algorithm to multi-dimensional wavelets results in a super-exponential increase in time complexity with the data dimensionality. Thus, we also introduce novel, polynomial-time approximation schemes (with tunable approximation guarantees for the target maximum-error metric) for deterministic wavelet thresholding in multiple dimensions.
1501195
On a bidirected relaxation for the MULTIWAY CUT problem
In the MULTIWAY CUT problem, we are given an undirected edge-weighted graph G = (V, E) with ce denoting the cost (weight) of edge e. We are also given a subset S of V, of size k, called the terminals. The objective is to find a minimum cost set of edges whose removal ensures that the terminals are disconnected.In this paper, we study a bidirected linear programming relaxation of MULTIWAY CUT. We resolve an open problem posed by Vazirani [Approximation Algorithms, first ed., Springer, Berlin, Heidelberg, 2001], and show that the integrality gap of this relaxation is not better than that for a geometric linear programming relaxation given by Calinescu et al. [J. Comput. System Sci. 60(3) (2000) 564-574], and may be strictly worse on some instances.
46840073
Better Algorithms for Minimizing Average Flow-Time on Related Machines
We consider the problem of minimising flow time on related machines and give an O(logP)-approximation algorithm for the offline case and an O(log2P)-competitive algorithm for the online version. This improves upon the previous best bound of O(log2P logS) on the competitive ratio. Here P is the ratio of the maximum to the minimum processing time of a job and S is the ratio of the maximum to the minimum speed of a machine.
8488383
Sorting and selection with structured costs
The study of the effect of priced information on basic algorithmic problems was initiated by M. Charikar et al. (2000). The authors continue the study of sorting and selection in the priced comparison model, i.e., when each comparison has an associated cost, and answer some of the open problems suggested by Charikar et al. If the comparison costs are allowed to be arbitrary, we show that one cannot get good approximation ratios. A different way to assign costs is based on the idea that one can distill out an intrinsic value for each item being compared, such that the cost of comparing two elements is some "well-behaved" or "structured" function of their values. We feel that most practical applications will have some structured cost property. The authors study the problems of sorting and selection (which includes finding the maximum and the median) in the structured cost model. We get a variety of approximation results for these problems, depending on the restrictions we put on the structured costs. We show that it is possible to get much improved results with the structured cost model than the case when we do not have any assumptions on comparison costs.
206560175
A constant-factor approximation algorithm for the multicommodity rent-or-buy problem
We present the first constant factor approximation algorithm for network design with multiple commodities and economies of scale. We consider the rent-or-buy problem, a type of multicommodity buy-at-bulk network design in which there are two ways to install capacity on any given edge. Capacity can be rented, with cost incurred on a per-unit of capacity basis, or bought, which allows unlimited use after payment of a large fixed cost. Given a graph and a set of source-sink pairs, we seek a minimum-cost way of installing sufficient capacity on edges so that a prescribed amount of flow can be sent simultaneously from each source to the corresponding sink. Recent work on buy-at-bulk network design has concentrated on the special case where all sinks are identical; existing constant factor approximation algorithms for this special case make crucial use of the assumption that all commodities ship flow to the same sink vertex and do not obviously extend to the multicommodity rent-or-buy problem. Prior to our work, the best heuristics for the multicommodity rent-or-buy problem achieved only logarithmic performance guarantees and relied on the machinery of relaxed metrical task systems or of metric embeddings. By contrast, we solve the network design problem directly via a novel primal-dual algorithm.
2443306
Long range dependence in network traffic and the closed loop behaviour of buffers under adaptive window control
We consider an Internet link carrying http-like traffic, i.e., transfers of finite volume files arriving at random time instants. These file transfers are controlled by an adaptive window protocol (AWP); an example of such a protocol is TCP. We provide analysis for the auto-covariance function of the AWP-controlled traffic into the link's buffer; this traffic, in general, cannot be represented by an on-off process. The analysis establishes that, for TCP-controlled transfer of Pareto-distributed file sizes with infinite second moment, the traffic into the link buffer is long range-dependent (LRD). We also develop an analysis for obtaining the stationary distribution of the link buffer occupancy under an AWP-controlled transfer of files sampled from some distribution. For any AWP, the analysis provides us with the Laplace-Stieltjes transform (LST) of the distribution of the link buffer occupancy process in terms of the functions defining the AWP and the file size distribution. The analysis also provides a necessary and a sufficient condition for the finiteness of the mean link buffer content; these conditions again have explicit dependence on the AWP used and the file size distribution. This establishes the sensitivity of the buffer occupancy process to the file size distribution. Combining the results from the above analyses, we provide various examples in which the closed loop control of an AWP results in finite mean link buffer occupancy even though the file sizes are Pareto-distributed (with infinite second moment), and the traffic into the link buffer is long range-dependent (with Hurst parameters which would suggest an infinite mean queue occupancy under open loop analysis). We also study the effect of window reductions due to active queue management and find that window reductions lead to further lightening of the tail of buffer occupancy distribution. The significance of this work is three-fold: (i) by looking at the window evolution as a function of the amount of data served and not as a function of time, this work provides a new framework for analysing various processes related to the link buffer under AWP-controlled transfer of files with a general file size distribution; (ii) it indicates that the buffer behaviour in the Internet may not be as poor as predicted from an open loop analysis of a queue fed with LRD traffic; and (iii) it shows that the buffer behaviour (and hence the throughput performance for finite buffers) is sensitive to the distribution of file sizes.
17761375
Comparative performance analysis of versions of TCP in a local network with a lossy link
We use a stochastic model to study the throughput performance of various transport control protocol (TCP) versions (Tahoe (including its older version that we call OldTahoe), Reno, and NewReno) in the presence of random losses on a wireless link in a local network. We model the cyclic evolution of TCP, each cycle starting at the epoch at which recovery starts from the losses in the previous cycle. TCP throughput is computed as the reward rate in a certain Markov renewal-reward process. Our model allows us to study the performance implications of various protocol features, such as fast retransmit and fast recovery. We show the impact of coarse timeouts. In the local network environment the key issue is to avoid a coarse timeout after a loss occurs. We show the effect of reducing the number of duplicate acknowledgements (ACKs) for triggering a fast retransmit. A large coarse timeout granularity seriously affects the performance of TCP, and the various protocol versions differ in their ability to avoid a coarse timeout when random loss occurs; we quantify these differences. We show that, for large packet-loss probabilities, TCP-Reno performs no better, or worse, than TCP-Tahoe. TCP-NewReno is a considerable improvement over TCP-Tahoe, and reducing the fast-retransmit threshold from three to one yields a large gain in throughput; this is similar to one of the modifications in the TCP-Vegas proposal. We explain some of these observations in terms of the variation of fast-recovery probabilities with packet-loss probability. The results of our analysis compare well with a simulation that uses actual TCP code.
1885434
Cost and availability tradeoffs in replicated data concurrency control
Techniques for optimizing a static voting type algorithm are presented. Our basic optimization models are based on minimizing communications cost subject to given reliability constraints. Two models are presented; in the first model the reliability constraint is failure tolerance, while in the second it is availability. Other simpler models that are special cases of these two basic models and rise from making simplifying assumptions such as equal vote values or constant inter-site communications costs are also discussed. We describe a semi-exhaustive algorithm and efficient heuristics for solving each model. The algorithms utilize a novel signature based method for identifying equivalent vote combinations, and an efficient procedure for computing availability. Computational results for the various algorithms are also given. Finally, the optimized static algorithm was compared against the available copies method, a dynamic algorithm, to understand the relative performance of the two types of algorithms. We found that if realistic reconfiguration times are assumed, then no one type of algorithm is uniformly better. The factors that influence relative performance have been identified. 16 refs., 2 figs., 10 tabs.
42238558
A crash recovery algorithm based on multiple logs that exploits parallelism
The paper describes an efficient algorithm for recovery based on multiple logs. The standard WAL algorithm is designed to work with a single log. Since each transaction is required to write a commit record to the log, it imposes limits on the maximum achievable throughput even if group commits are allowed. These limits are well below the needs of high transaction rate systems in airlines and in other areas. Another problem with a 'single log' algorithm is that the tail of the log is a 'hot spot' because of severe contention for it. It is shown that both these problems are solved by extending the write-ahead logging method into a multiple log algorithm which allows transactions to write to one of several logs, and also permits each log to perform checkpoints and I/O operations in parallel. A further advantage of multiple logs is that parallelism can be exploited at recovery time. An algorithm is outlined that speeds up recovery by scanning the multiple logs in parallel.<<ETX>>
17013178
Smart supply web: an application of web-based data and workflow mediation
This paper describes our vision of a Supply Web as the next major advance in the e-commerce world in terms of how e-services are delivered. After highlighting shortcomings of existing supply chain solutions, we give an architecture to show how three important technologies, namely, workow systems, data integration and on-line decision support, will have to come together to enable seamless deployment of e-service supply web solutions. We rst discuss research eorts (namely, XRL, YAT and DecisionFlows) that support the three technologies separately, and then describe the challenges of integrating them eectively.