1411225
Provisioning a virtual private network: a network design problem for multicommodity flow
Consider a setting in which a group of nodes, situated in a large underlying network, wishes to reserve bandwidth on which to support communication. Virtual private networks (VPNs) are services that support such a construct; rather than building a new physical network on the group of nodes that must be connected, bandwidth in the underlying network is reserved for communication within the group, forming a virtual “sub-network.”
Provisioning a virtual private network over a set off terminals gives rise to the following general network design problem. We have bounds on the cumulative amount of traffic each terminal can send and receive; we must choose a path for each pair of terminals, and a bandwidth allocation for each edge of the network, so that any traffic matrix consistent with the given upper bounds can be feasibly routed. Thus, we are seeking to design a network that can support a continuum of possible traffic scenarios.
We provide optimal and approximate algorithms for several variants of this problem, depending on whether the traffic matrix is required to be symmetric, and on whether the designed network is required to be a tree (a natural constraint in a number of basic applications). We also establish a relation between this collection of network design problems and a variant of the facility location problem introduced by Karger and Minkoff; we extend their results by providing a stronger approximation algorithm for this latter problem.
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.
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.
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.
9913363
Leveraging Information Sharing to Increase Supply Chain Configurability
As supply chains evolve beyond the confines of individual organizations, collaboration has become the Holy Grail in supply chain technology. It plays a key role in achieving flexibility and responsiveness. Information sharing between partners is a key determinant of collaboration. This paper investigates information sharing in four different supply chains—3PL, VMI, CPFR, and supply networks—and compares their information sharing structures, shared data objects, and information flow models. The results show how the various parameters of an information flow model constrain the level of collaboration. Further, the modeling exercise provides insights on how to configure a collaborative supply chain by leveraging information sharing.
7308298
Data streaming algorithms for accurate and efficient measurement of traffic and flow matrices
The traffic volume between origin/destination (OD) pairs in a network, known as traffic matrix, is essential for efficient network provisioning and traffic engineering. Existing approaches of estimating the traffic matrix, based on statistical inference and/or packet sampling, usually cannot achieve very high estimation accuracy. In this work, we take a brand new approach in attacking this problem. We propose a novel data streaming algorithm that can process traffic stream at very high speed (e.g., 40 Gbps) and produce traffic digests that are orders of magnitude smaller than the traffic stream. By correlating the digests collected at any OD pair using Bayesian statistics, the volume of traffic flowing between the OD pair can be accurately determined. We also establish principles and techniques for optimally combining this streaming method with sampling, when sampling is necessary due to stringent resource constraints. In addition, we propose another data streaming algorithm that estimates flow matrix, a finer-grained characterization than traffic matrix. Flow matrix is concerned with not only the total traffic between an OD pair (traffic matrix), but also how it splits into flows of various sizes. Through rigorous theoretical analysis and extensive synthetic experiments on real Internet traffic, we demonstrate that these two algorithms can produce very accurate estimation of traffic matrix and flow matrix respectively.
1111647
Performance Evaluation of an Operating System Transaction Manager
A conventional transaction manager implemented by a database management system (DBMS) was compared against one implemented within an operating system (OS) in a variety of simulated situations. Models of concurrency control and crash recovery were constructed for both environments, and the results of a collection of experiments are presented in this paper. The results indicate that an OS transaction manager incurs a severe performance disadvantage and appears to be feasible only in special circumstances.
2987975
Data streaming algorithms for efficient and accurate estimation of flow size distribution
Knowing the distribution of the sizes of traffic flows passing through a network link helps a network operator to characterize network resource usage, infer traffic demands, detect traffic anomalies, and accommodate new traffic demands through better traffic engineering. Previous work on estimating the flow size distribution has been focused on making inferences from sampled network traffic. Its accuracy is limited by the (typically) low sampling rate required to make the sampling operation affordable. In this paper we present a novel data streaming algorithm to provide much more accurate estimates of flow distribution, using a "lossy data structure" which consists of an array of counters fitted well into SRAM. For each incoming packet, our algorithm only needs to increment one underlying counter, making the algorithm fast enough even for 40 Gbps (OC-768) links. The data structure is lossy in the sense that sizes of multiple flows may collide into the same counter. Our algorithm uses Bayesian statistical methods such as Expectation Maximization to infer the most likely flow size distribution that results in the observed counter values after collision. Evaluations of this algorithm on large Internet traces obtained from several sources (including a tier-1 ISP) demonstrate that it has very high measurement accuracy (within 2%). Our algorithm not only dramatically improves the accuracy of flow distribution measurement, but also contributes to the field of data streaming by formalizing an existing methodology and applying it to the context of estimating the flow-distribution.
39839954
A randomized algorithm for distributed consensus
We describe a randomized, fully distributed algorithm for distributed consensus and evaluate its performance assuming probabilistically bounded message delay. Each node randomly contacts a few other nodes and incorporates their values into its own value. All the nodes are able to reach consensus in this manner after a few rounds. The results show that the randomized algorithm is flexible, efficient and robust, and offers several advantages over a deterministic algorithm.