757091
Efficient Job Scheduling Algorithms with Multi-type Contentions
In this paper, we consider an interesting generalization of the classic job scheduling problem in which each job needs to compete for not only machines but also other types of resources The contentions among jobs for machines and resources could interfere with each other, which complicates the problem dramatically We present a family of approximation algorithms for solving several variants of the problem by using a generic algorithmic framework Our algorithms achieve a constant approximation ratio (i.e., 3) if there is only one type of resources or certain dependency relation exists among multiple types of resources For the case that r unrelated resources are given, the approximation ratio of our algorithm becomes k + 2, where k ≤ r is a constant depending on the problem instance As an application, we also show that our techniques can be easily applied to optical burst switching (OBS) networks for deriving more efficient wavelength scheduling algorithms.
21098955
Topological Peeling and Implementation
We present a new approach, called topological peeling, and its implementation for traversing a portion AR of the arrangement formed by n lines within a convex region R on the plane. Topological peeling visits the cells of AR in a fashion of propagating a "wave" of a special shape (called a double-wriggle curve) starting at a single source point. This special traversal fashion enables us to solve several problems (e.g., computing shortest paths) on planar arrangements to which previously best known arrangement traversal techniques such as topological sweep and topological walkm ay not be directly applicable. Our topological peeling algorithm takes O(K + n log(n + r)) time and O(n + r) space, where K is the number of cells in AR and r is the number of boundary vertices of R. Comparing with topological walk, topological peeling uses a simpler and more efficient way to sweep different types of lines, and relies heavily on exploring small local structures, rather than a much larger global structure. Experiments show that, on average, topological peeling outperforms topological walkb y 10 - 15% in execution time.
14297439
Geometric permutations of high dimensional spheres
We prove the maximum number of geometric permutations, induced by line transversals to a set of <i>n</i> pairwise disjoint congruent spheres in <i>R<sup>d</sup></i> with <i>d</i> ⪈ 3, is no more than 4 when <i>n</i> is sufficiently large, achieving the best known upper bound for this problem. We also prove the maximum number of geometric permutations of a set of <i>n</i> noncongruent spheres of bounded radius ratio in R<sup>d</sup>, <i>d</i> ⪈ 3, is at most 2<sup>[√2<i>M</i>]+1</sup>, where <i>M</i> is the ratio or the largest radius and the smallest radius. Our result settles a conjecture in combinatorial geometry.
29728094
Graph Bandwidth of Weighted Caterpillars
Graph bandwidth minimization (GBM) is a classical and challenging problem in graph algorithms and combinatorial optimization. Most of existing researches on this problem have focused on unweighted graphs. In this paper, we study the bandwidth minimization problem of weighted caterpillars, and propose several algorithms for solving various types of caterpillars and general graphs. More specifically, we show that the GBM problem on caterpillars with hair-length at most 2 and the GBM problem on star-shape caterpillars are NP-complete, and give a lower bound of the graph bandwidth for general weighted graphs. For caterpillars with hair-length at most 1, we present an O(n log n log(nwmax))-time algorithm to compute an optimal bandwidth layout, where n is the total number of vertices in the graph and wmax is the maximum wedge weight. For caterpillars with hair-length at most k, we give a k-approximation algorithm. For arbitrary caterpillars and general graphs, we give a heuristic algorithm and some experimental results. Experiments show that the solutions obtained by our heuristic algorithm are roughly within a factor of c log(n) of the lower bound for a small number c, which is consistent with the inapproximability results of this problem (i.e., no constant approximation for the GBM problem unless P = NP). © 2006 Published by Elsevier B.V.
6260724
Finding an optimal path without growing the tree
For problems on computing an optimal path as well as its length in a certain setting, the "standard" approach for finding an actual optimal path is by building (or "growing") a single-source optimal path tree. In this paper, we study a class of optimal path problems with the following phenomenon: The space complexity of the algorithms for reporting the lengths of single-source optimal paths for these problems is asymptotically smaller than the space complexity of the "standard" tree-growing algorithms for finding actual optimal paths. We present a general and efficient algorithmic paradigm for finding an actual optimal path for such problems without having to grow a single-source optimal path tree. Our paradigm is based on the "marriage-before-conquer" strategy, the prune-and-search technique, and a new data structure called clipped trees. The paradigm enables us to compute an actual path for a number of optimal path problems and dynamic programming problems in computational geometry, graph theory, and combinatorial optimization. Our algorithmic solutions improve the space bounds (in certain cases, the time bounds as well) of the previously best known algorithms, and settle some open problems. Our techniques are likely to be applicable to other problems.
28240465
Motion Tracking and Intensity Surface Recovery in Microscopic Nuclear Images
Current techniques for microscopic imaging do not provide necessary spatial and temporal resolutions for real time visualization of the nucleus. Images can only be acquired in time lapse mode, leading to significant loss of information between image frames. Such data, if available, can be extremely helpful in the study of nuclear organization and function. In this paper, we present a gamut of geometric-technique-based approaches for solving the problem. Our techniques, working together, can effectively recover complicated motion and deformation as well as the change of intensity surfaces from pairs of images in a microscopic image sequence, and has low time complexity, particularly desirable by many biological applications where large amount of DNA need to be processed. These techniques are also readily applicable to other types of images for reconstructing motion and intensity surfaces of deformable objects.
12832200
A unified proof of minimum time complexity for reaching consensus and uniform consensus - an oracle-based approach
In this paper, we offer new proofs to two lower bound results in distributed computing: a minimum of f+1 and f+2 rounds for reaching consensus and uniform consensus respectively when at most f fail-stop faults can happen. Here the computation model is synchronous message passing. Both proofs are based on a novel oracle argument. These two induction proofs are unified in the following sense: the induction steps are the same and only the initial step (f=0) needs to be proved separately. The techniques used in the proof offer new insights into the lower bound results in distributed computing.
26863394
A Firewalling Scheme for Securing MPOA-Based Enterprise Networks
A well-known security problem with MPOA is that cut-through connections generally bypasses firewall routers if there are any. None of the previously proposed approaches solved the problem properly. In this paper, we propose a novel firewalling scheme for MPOA that nicely fixes the security hole. Our firewalling scheme has three outstanding advantages that make it ideal for securing MPOA-based enterprise networks. First, based on our novel concept of "logical chokepoints", our firewalling scheme does not require the existence of physical chokepoints inside the network. Second, the scheme is nicely embedded into the MPOA protocol so that its cost, performance overhead, and protocol complexity are reduced to a minimum. Third, the scheme is centrally administered so that it scales well to very large networks.
15426263
Super connectivity of line graphs
The super connectivity κ' and the super edge-connectivity λ' are more refined network reliability indices than connectivity κ and edge-connectivity λ. This paper shows that for a connected graph G with order at least four rather than a star and its line graph L(G), κ'(L(G)) = λ'(G) if and only if G is not super-λ'. As a consequence, we obtain the result of Hellwig et al. [Note on the connectivity of line graphs, Inform. Process. Lett. 91 (2004) 7] that κ(L(G)) = λ'(G). Furthermore, the authors show that the line graph of a super-λ' graph is super-λ if the minimum degree is at least three.
240982
Data streaming algorithms for estimating entropy of network traffic
Using entropy of traffic distributions has been shown to aid a wide variety of network monitoring applications such as anomaly detection, clustering to reveal interesting patterns, and traffic classification. However, realizing this potential benefit in practice requires accurate algorithms that can operate on high-speed links, with low CPU and memory requirements. In this paper, we investigate the problem of estimating the entropy in a streaming computation model. We give lower bounds for this problem, showing that neither approximation nor randomization alone will let us compute the entropy efficiently. We present two algorithms for randomly approximating the entropy in a time and space efficient manner, applicable for use on very high speed (greater than OC-48) links. The first algorithm for entropy estimation is inspired by the structural similarity with the seminal work of Alon et al. for estimating frequency moments, and we provide strong theoretical guarantees on the error and resource usage. Our second algorithm utilizes the observation that the performance of the streaming algorithm can be enhanced by separating the high-frequency items (or elephants) from the low-frequency items (or mice). We evaluate our algorithms on traffic traces from different deployment scenarios.
7186877
On replica placement for QoS-aware content distribution
The rapid growth of time-critical information services and business-oriented applications is making quality of service (QoS) support increasingly important in content distribution. This paper investigates the problem of placing object replicas (e.g., web pages and images) to meet the QoS requirements of clients with the objective of minimizing the replication cost. We consider two classes of service models: replica-aware service and replica-blind service. In the replica-aware model, the servers are aware of the locations of replicas and can therefore direct requests to the nearest replica. We show that the QoS-aware placement problem for replica-aware services is NP-complete. Several heuristic algorithms for efficient computation of suboptimal solutions are proposed and experimentally evaluated. In the replica-blind model, the servers are not aware of the locations of replicas or even their existence. As a result, each replica only serves the requests flowing through it under some given routing strategy. We show that there exist polynomial optimal solutions to the QoS-aware placement problem for replica-blind services. Efficient algorithms are proposed to compute the optimal locations of replicas under different cost models.