7719957
Connectivity and inference problems for temporal networks
Many network problems are based on fundamental relationships involving time. Consider, for example, the problems of modeling the flow of information through a distributed network, studying the spread of a disease through a population, or analyzing the reachability properties of an airline timetable. In such settings, a natural model is that of a graph in which each edge is annotated with a time label specifying the time at which its endpoints "communicated." We will call such a graph a temporal network. To model the notion that information in such a network "flows" only on paths whose labels respect the ordering of time, we call a path time-respecting if the time labels on its edges are non-decreasing. The central motivation for our work is the following question: how do the basic combinatorial and algorithmic properties of graphs change when we impose this additional temporal condition? The notion of a path is intrinsic to many of the most fundamental algorithmic problems on graphs; spanning trees, connectivity, flows, and cuts are some examples. When we focus on time-respecting paths in place of arbitrary paths, many of these problems acquire a character that is different from the traditional setting, but very rich in its own right. We provide results on two types of problems for temporal networks. First, we consider connectivity problems, in which we seek disjoint time-respecting paths between pairs of nodes. The natural analogue of Menger's Theorem for node-disjoint paths fails in general for time-respecting paths; we give a non-trivial characterization of those graphs for which the theorem does hold in terms of an excluded subdivision theorem, and provide a polynomial-time algorithm for connectivity on this class of graphs. (The problem on general graphs is NP-complete.) We then define and study the class of inference problems, in which we seek to reconstruct a partially specified time labeling of a network in a manner consistent with an observed history of information flow.
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.
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.
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.
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.
8290753
Time and energy complexity of distributed computation in wireless sensor networks
We consider a scenario where a wireless sensor network is formed by randomly deploying n sensors to measure some spatial function over a field, with the objective of computing the maximum value of the measurements and communicating it to an operator station. We view the problem as one of message passing distributed computation over a geometric random graph. The network is assumed to be synchronous; at each sampling instant each sensor measures a value, and then the sensors collaboratively compute and deliver the maximum of these values to the operator station. Computation algorithms differ in the messages they need to exchange, and our formulation focuses on the problem of scheduling of the message exchanges. We do not exploit techniques such as source compression, or block coding of the computations. For this problem, we study the computation time and energy expenditure for one time maximum computation, and also the pipeline throughput. We show that, for an optimal algorithm, the computation time, energy expenditure and the achievable rate of computation scale as /spl Theta/(/spl radic/ n/log n), /spl Theta/(n) and /spl Theta/(1/log n) asymptotically (in probability) as the number of sensors n/spl rarr//spl infin/. We also analyze the performance of three specific computational algorithms, namely, the tree algorithm, multihop transmission, and the ripple algorithm, and obtain scaling laws for the computation time and energy expenditure as n/spl rarr//spl infin/. Simulation results are provided to show that our analysis indeed captures the correct scaling; the simulations also yield estimates of the constant multipliers in the scaling laws. Our analyses throughout assume a centralized scheduler and hence our results can be viewed as providing bounds for the performance with a distributed scheduler.
433794
A Framework for Document-Driven Workflow Systems
We propose and demonstrate the feasibility of a framework for document-driven workflow systems that requires no explicit control flow and the execution of the process is driven by input documents. The framework can assist workflow designers to discover the data dependencies between tasks in a process and achieve more efficient control flow design. The framework also provides an architecture to separate the workflow system from application data and facilitate inter-organizational processes. Document-driven workflow systems are more flexible than traditional control flow processes, easier to verify and work better for ad hoc workflows. We also implemented a prototype workflow system using the framework entirely in a RDBMS using Transact-SQL in Microsoft SQL Server 2000. A detailed comparison with control driven workflows has also been done.
37821202
Optimizing Voting-Type Algorithms for Replicated Data
The main objectives of data replication are improved availability and reduced communications cost for queries. Maintaining the various copies consistent, however, increases the communications cost incurred by updates. For a given degree of replication, the choice of a specific concurrency control algorithm can have a significant impact on the total communications cost. In this paper we present various models for analyzing and understanding the trade-offs between the potentially opposing objectives of maximum resiliency and minimum communications cost in the context of the quorum consensus class of algorithms. It is argued that an optimal vote assignment is one which meets given resiliency goals and yet incurs the least communications cost compared with all other alternative assignments. A mathematical model for vote assignment is developed, and optimal algorithms are presented. It is demonstrated that significant cost savings can be realized from these approaches.
39824506
An analysis of borrowing policies for escrow transactions in a replicated data environment
Three issues in the context of escrow-based methods, are addressed. It is shown that full serializability can be guaranteed for escrow transactions by means of repeat semantics, that is, a transaction which fails is rerun in a special mode. The author describes a crash recovery protocol consistent with the concurrency control scheme used. An analysis is made, by means of a simulation model, of several different borrowing policies for escrow transactions and the best one is identified.<<ETX>>
2583878
A data streaming algorithm for estimating subpopulation flow size distribution
Statistical information about the flow sizes in the traffic passing through a network link helps a network operator to characterize network resource usage, infer traffic demands, detect traffic anomalies, and improve network performance through traffic engineering. Previous work on estimating the flow size distribution for the complete population of flows has produced techniques that either make inferences from sampled network traffic, or use data streaming approaches. In this work, we identify and solve a more challenging problem of estimating the size distribution and other statistical information about arbitrary subpopulations of flows. Inferring subpopulation flow statistics is more challenging than the complete population counterpart, since subpopulations of interest are often specified a posteriori (i.e., after the data collection is done), making it impossible for the data collection module to "plan in advance".Our solution consists of a novel mechanism that combines data streaming with traditional packet sampling to provide highly accurate estimates of subpopulation flow statistics. The algorithm employs two data collection modules operating in parallel --- a NetFlow-like packet sampler and a streaming data structure made up of an array of counters. Combining the data collected by these two modules, our estimation algorithm uses a statistical estimation procedure that correlates and decodes the outputs (observations) from both data collection modules to obtain flow statistics for any arbitrary subpopulation. Evaluations of this algorithm on real-world Internet traffic traces demonstrate its high measurement accuracy.