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.
2872380
Building Edge-Failure Resilient Networks
AbstractWe consider the design of resilient networks that are fault tolerant
 against link failures. Resilience against link failures can be built
 into the network by providing backup paths, which are used in
 the eventuality of an edge failure occurring on a primary path in the
 network. We consider several network design problems in this context;
 these problems are motivated by the requirements of current high-speed
 optical networks. In all the following problems the objective is to
 provide resilience in networks while minimizing the cost incurred.
 The main problem under consideration in this paper is that of backup
 allocation: this problem takes as its input an already provisioned 
 primary network and a parameter k, and allocates backup capacity 
 on the edges of the underlying network so that all the demand can be 
 routed even in the presence of k edge failures. We also consider a 
 variant of this problem where the primary network has a tree topology, 
 and it is required that the restored network retains a tree topology. 
 We then address the problem of simultaneous primary and backup
 allocation: we are given specifications of the traffic to be
 handled, and the goal is to provision both the primary as well as
 the backup network. Finally, we investigate a single-commodity
 problem motivated by a pragmatic scenario in which the primary
 network is not known in advance and demands between source--sink
 pairs arrive online.
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.
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.
1630993
Join-distinct aggregate estimation over update streams
There is growing interest in algorithms for processing andquerying continuous data streams (i.e., data that is seenonly once in a fixed order) with limited memory resources.Providing (perhaps approximate) answers to queries over suchstreams is a crucial requirement for many application environments;examples include large IP network installations where performancedata from different parts of the network needs to be continuouslycollected and analyzed.
The ability to estimate the number of distinct (sub)tuples inthe result of a join operation correlating two data streams (i.e.,the cardinality of a projection with duplicate elimination over ajoin) is an important requirement for several data-analysisscenarios. For instance, to enable real-time traffic analysis andload balancing, a network-monitoring application may need toestimate the number of distinct (<i>source</i>,destination) IP-address pairs occurring in the stream of IP packetsobserved by router <i>R</i><inf>1</inf>,where the source address is also seen in packets routed through adifferent router <i>R</i><inf>2</inf>.Earlier work has presented solutions to the individual problems ofdistinct counting and join-size estimation (without duplicateelimination) over streams. These solutions, however, arefundamentally different and extending or combining them to handleour more complex "Join-Distinct" estimation problem is far fromobvious. In this paper, we propose the <i>first</i>space-efficient algorithmic solution to the general Join-Distinctestimation problem over continuous data streams (our techniques canactually handle general <i>update streams</i>comprising tuple deletions as well as insertions). Our estimatorsare probabilistic in nature and rely on novel algorithms forbuilding and combining a new class of hash-based synopses (termed"JD <i>sketches</i>") for individual update streams. Wedemonstrate that our algorithms can provide low error,high-confidence Join-Distinct estimates using only small space andsmall processing time per update. In fact, we present lower boundsshowing that the space usage of our estimators is within smallfactors of the best possible for the Join-Distinct problem.Preliminary experimental results verify the effectiveness of ourapproach.
206590820
Structure from Motion with Known Camera Positions
The wide availability of GPS sensors is changing the landscape in the applications of structure from motion techniques for localization. In this paper, we study the problem of estimating camera orientations from multiple views, given the positions of the viewpoints in a world coordinate system and a set of point correspondences across the views. Given three or more views, the above problem has a finite number of solutions for three or more point correspondences. Given six or more views, the problem has a finite number of solutions for just two or more points. In the three-view case, we show the necessary and sufficient conditions for the three essential matrices to be consistent with a set of known baselines. We also introduce a method to recover the absolute orientations of three views in world coordinates from their essential matrices. To refine these estimates we perform a least-squares minimization on the group cross product SO(3) × SO(3) × SO(3). We report experiments on synthetic data and on data from the ICCV2005 Computer Vision Contest.
5840162
The Case for Non-Cooperative Multihoming of Users to Access Points in IEEE 802.11 WLANs
In many cases, a mobile user has the option of connecting to one of several IEEE 802.11 access points (APs),each using an independent channel. User throughput in each 
AP is determined by the number of other users as well as the 
frame size and physical rate being used. We consider the scenario where users could multihome, i.e., split their traffic amongst all the available APs, based on the throughput they obtain and the price charged. Thus, they are involved in a non-cooperative game with each other. We convert the problem into a fluid model and show that under a pricing scheme, which we call the cost price mechanism, the total system throughput is maximized,i.e., the system suffers no loss of efficiency due to selfish dynamics. We also study the case where the Internet Service 
Provider (ISP) could charge prices greater than that of the cost price mechanism. We show that even in this case multihoming outperforms unihoming, both in terms of throughput as well as profit to the ISP.
33509544
Multiscale rough set data analysis with application to stock performance modeling
Multiscale Rough Set Data Analysis (MSRSDA) combines the feature selection and feature extraction ability of RSDA with the multiresolution property of the wavelet transform. RSDA removes the irrelevant (having no impact on prediction performance) and dependent (having no discriminatory power) market variables from the multivariate time series data matrix, thereby improving generalization capability of the forecasting engine (neural network, fuzzy inference system). A wavelet transform is used to decompose the time series into varying scales of resolution so that the underlying temporal structures of the original time series become more tractable; the decomposition is additive in details and approximation. Significance of market variables at various wavelet scales representing "detailed" short-term history and "general" long-term history of the time series, is computed using RSDA in wavelet space. Irrelevant and redundant variables at each scale are removed and a forecasting engine is then trained on each of the relevant resolution scales (i.e., those scales where significant events are detected); individual wavelets forecasts are recombined to form the overall forecast. The superior performance of MSRSDA is illustrated through stock performance modeling example. For prediction of S&P500 index, a data matrix of 21 variables has been used. MSRSDA gives 69% accuracy on stock-trend prediction.
2753181
Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data
A novel algorithm for managing replicated data is presented. The proposed method is based on organizing the copies of an object into a logical, multilevel hierarchy, and extending the quorum consensus algorithm to such an environment. Several properties of the method are derived and optimality conditions are given for minimizing the quorum size. It is shown that, given a collection of n copies of an object, the method allows a quorum to be formed with n/sup 0.63/ copies versus ((n+1)/2) copies in the case of the majority voting algorithm. Tradeoffs between the proposed method and three other quorum-based methods are discussed, and the main features of each method are highlighted. >
206778468
A performance study of general grid structures for replicated data
Recently, there has been considerable interest in the study of replica-control protocols which are based on organizing several copies of an object into logical structures, such as rectangular grids. In addition to high availability, another objective in exploiting such structures is to improve the degree of load sharing in a system. The authors extend the scope of grid structures to general grids, which allow holes in various positions of a rectangular structure and are useful to consider because they often produce availabilities that are higher than solid grids, where every position must be occupied by a node. In addition to proposing an improvement to the existing grid protocol, new insights are offered into the performance of the grids, from both availability and load sharing points of view. Algorithms for designing grids to maximize availability independently and also in conjunction with a load sharing constraint are given.<<ETX>>