47268289
Optimal configuration of OSPF aggregates
Open Shortest Path First (OSPF) is a popular protocol for routing within an autonomous system (AS) domain. In order to scale for large networks containing hundreds and thousands of subnets, OSPF supports a two-level hierarchical routing scheme through the use of OSPF areas. Subnet addresses within an area are aggregated, and this aggregation is a crucial requirement for scaling OSPF to large AS domains, as it results in significant reductions in routing table sizes, smaller link-state databases, and less network traffic to synchronize the router link-state databases. On the other hand, address aggregation also implies loss of information about the length of the shortest path to each subnet, which in turn, can lead to suboptimal routing.In this paper, we address the important practical problem of configuring OSPF aggregates to minimize the error in OSPF shortest-path computations due to subnet aggregation. We first develop an optimal dynamic programming algorithm that, given an upper bound k on the number of aggregates to be advertised and a weight assignment function for the aggregates, computes the k aggregates that result in the minimum cumulative error in the shortest-path computations for all source-destination subnet pairs. Subsequently, we tackle the problem of assigning weights to OSPF aggregates such that the cumulative error in the computed shortest paths is minimized. We demonstrate that, while for certain special cases (e.g., unweighted cumulative error) efficient optimal algorithms for the weight assignment problem can be devised, the general problem itself is NP-hard. Consequently, we have to rely on search heuristics to solve the weight assignment problem. To the best of our knowledge, our work is the first to address the algorithmic issues underlying the configuration of OSPF aggregates and to propose efficient configuration algorithms that are provably optimal for many practical scenarios.
46145059
Primal-Dual Algorithms for Connected Facility Location Problems
We consider the Connected Facility Location problem. We are given a graph G = (V, E) with cost ce on edge e, a set of facilities F ? V, and a set of demands D ? V. We are also given a parameter M ? 1. A solution opens some facilities, say F, assigns each demand j to an open facility i(j), and connects the open facilities by a Steiner tree T. The cost incurred is ?i?F fi + ?j?D djci(j)j + M ?e?T ce. We want a solution of minimum cost. A special case is when all opening costs are 0 and facilities may be opened anywhere, i.e., F = V. If we know a facility v that is open, then this problem reduces to the rent-or-buy problem. We give the first primal-dual algorithms for these problems and achieve the best known approximation guarantees. We give a 9-approximation algorithm for connected facility location and a 5-approximation for the rent-or-buy problem. Our algorithm integrates the primal-dual approaches for facility location [7] and Steiner trees [1,2]. We also consider the connected k-median problem and give a constant-factor approximation by using our primal-dual algorithm for connected facility location. We generalize our results to an edge capacitated version of these problems.
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.
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.
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.
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>>
1151748
Scalable and Efficient Data Streaming Algorithms for Detecting Common Content in Internet Traffic
Recent research on data streaming algorithms has provided powerful tools to efficiently monitor various characteristics of traffic passing through a single network link or node. However, it is often desirable to perform data streaming analysis on the traffic aggregated over hundreds or even thousands of links/nodes, which will provide network operators with a holistic view of the network operation. Shipping raw traffic data to a centralized location (i.e., “raw aggregation”) for streaming analysis is clearly not a feasible approach for a large network. In this paper, we propose a set of novel distributed data streaming algorithms that allow scalable and efficient monitoring of aggregated traffic without the need for raw aggregation. Our algorithms target the specific network monitoring problem of finding common content in the Internet traffic traversing several nodes/links, which has applications in network-wide intrusion detection, early warning for fast propagating worms, and detection of hot objects and spam traffic. We evaluate our algorithms through extensive simulations and experiments on traffic traces collected from a tier-1 ISP. The experimental results demonstrate that our algorithms can effectively detect common content in the traffic traversing across a large network.
14310908
HPP: A Reliable Causal Broadcast Protocol for Large-Scale Replication
This paper describes a fast, reliable, scalable and efficient broadcast protocol called HPP (hierarchical propagation protocol) for weak-consistency replica management. It is based on organizing the nodes in a network into a logical hierarchy and maintaining a limited amount of state information at each node. It ensures that messages are not lost due to failures or partitions and minimizes redundancy. Furthermore, the protocol allows messages to be diffused while nodes are down provided the parent and child nodes of a failed node are alive. Moreover, the protocol allows nodes to be moved in the logical hierarchy and the network to be restructured dynamically in order to improve performance, while still ensuring that no messages are lost while the switch takes place and without disturbing normal operation. A performance study of the protocol in terms of availability and propagation delay indicates that the protocol reduces the delay by a factor of four compared to a protocol that does not diffuse messages past failed nodes.
15446858
A new approach for asynchronous distributed rate control of elastic sessions in integrated packet networks
We develop a new class of asynchronous distributed algorithms for the explicit rate control of elastic sessions in an integrated packet network. Sessions can request for minimum guaranteed rate allocations (e.g., minimum cell rates in the ATM context), and, under this constraint, we seek to allocate the max-min fair rates to the sessions. We capture the integrated network context by permitting the link bandwidths available to elastic sessions to be stochastically time varying. The available capacity of each link is viewed as some statistic of this stochastic process [e.g., a fraction of the mean, or a large deviations-based equivalent service capacity (ESC)]. The ESC is obtained so as to satisfy an overflow probability constraint on the buffer length. For fixed available capacity at each link, we show that the vector of max-min fair rates can be computed from the root of a certain vector equation. A distributed asynchronous stochastic approximation technique is then used to develop a provably convergent distributed algorithm for obtaining the root of the equation, even when the link flows and the available capacities are obtained from on-line measurements. The switch algorithm does not require per connection monitoring, nor does it require per connection marking of control packets. A virtual buffer based approach for on-line estimation of the ESC is utilized. We also propose techniques for handling large variations in the available capacity owing to the arrivals or departures of CBR/VBR sessions. Finally, simulation results are provided to demonstrate the performance of this class of algorithms in the local and wide area network context.
14111853
An analytical state dependent leakage power model for FPGAs
In this paper we present a state dependent analytical leakage power model for FPGAs. The model accounts for subthreshold leakage and gate leakage in FPGAs, since these are the two dominant components of total leakage power. The power model takes into account the dependency of gate and subthreshold leakage on the probability of the state of circuit inputs. The leakage power model has two main components, one which computes the probability of a state for a particular FPGA circuit element, and the other which computes the leakage of the FPGA circuit element for a given input using analytical equations. This FPGA power model is particularly important for rapidly analyzing various FPGA architectures across different technology nodes