9742261
Portable and Efficient Parallel Computing Using the BSP Model
The Bulk-Synchronous Parallel (BSP) model was proposed by Valiant as a standard interface between parallel software and hardware. In theory, the BSP model has been shown to allow the asymptotically optimal execution of architecture independent software on a variety of architectures. Our goal in this work is to experimentally examine the practical use of the BSP model on current parallel architectures. We describe the design and implementation of the Green BSP Library, a small library of functions that implement the BSP model, and of several applications that were written for this library. We then discuss the performance of the library and application programs on several parallel architectures. Our results are positive in that we demonstrate efficiency and portability over a range of parallel architectures and show that the BSP cost model is useful for predicting performance trends and estimating execution times.
96030
Beyond the flow decomposition barrier
We introduce a new approach to the maximum flow problem. This approach is based on assigning arc lengths based on the residual flow value and the residual arc capacities. Our approach leads to an <italic>O</italic>(min(<italic>n</italic><supscrpt>2/3</supscrpt>, <italic>m</italic><supscrpt>1/2</supscrpt>)<italic>m</italic> log(<italic>n</italic><supscrpt>2</supscrpt>/<italic>m</italic>) log <italic>U</italic>) time bound for a network with <italic>n</italic> vertices, <italic>m</italic> arcs, and integral arc capacities in the range [1, …, <italic>U</italic>]. This is a fundamental improvement over the previous time bounds. We also improve bounds for the Gomory-Hu tree problem, the parametric flow problem, and the approximate <italic>s-t</italic>  cut problem.
10307808
A tight bound on approximating arbitrary metrics by tree metrics
In this paper, we show that any n point metric space can be embedded into a distribution over dominating tree metrics such that the expected stretch of any edge is O(log n). This improves upon the result of Bartal who gave a bound of O(log n log log n). Moreover, our result is existentially tight; there exist metric spaces where any tree embedding must have distortion Ω(log n)-distortion. This problem lies at the heart of numerous approximation and online algorithms including ones for group Steiner tree, metric labeling, buy-at-bulk network design and metrical task system. Our result improves the performance guarantees for all of these problems.
34346796
Beyond the flow decomposition barrier
We introduce a new approach to the maximum flow problem. This approach is based on assigning arc lengths based on the residual flow value and the residual are capacities. Our approach leads to an O(min(n/sup 2/3/, m/sup 1/2/)m log(n/sup 2//m) log U) time bound for a network with n vertices, m arcs, and integral arc capacities in the range [1,...,U]. This is a fundamental improvement over the previous time bounds. We also improve bounds for the Gomory-Hu tree problem, the parametric flow problem, and the approximate s-t cut problems.
7001903
Distributed object location in a dynamic network
Modern networking applications replicate data and services widely, leading to a need for location-independent routing -- the ability to route queries directly to objects using names independent of the objects' physical locations. Two important properties of a routing infrastructure are routing locality and rapid adaptation to arriving and departing nodes. We show how these two properties can be efficiently achieved for certain network topologies. To do this, we present a new distributed algorithm that can solve the nearest-neighbor problem for these networks. We describe our solution in the context of Tapestry, an overlay network infrastructure that employs techniques proposed by Plaxton, Rajaraman, and Richa [14].
15983187
Small distortion and volume preserving embeddings for planar and Euclidean metrics
A finite metric space, (S,d) , contains a finite set of points and a distance function on pairs of points. A contraction is an embedding, h, of a finite metric space (S, d) into Rd where for any u, v E S, the Euclidean (&) distance between h(u) and h(v) is no more than d(u, v). The distortion of the embedding is the maximum over pairs of the ratio of d(u, w) and the Euclidean distance between h(u) and h(v). Bourgain showed that any graphical metric could be embedded with distortion O(logn). Linial, London and Rabinovich and Aumman and Rabani used such embeddings to prove an O(log k) approximate max-flow min-cut theorem for k commodity flow problems. A generalization of embeddings that preserve distances between pairs-of points are embeddings that preserve volumes of larger sets. In particular, A (k, c)-volume respecting embedding of n-points in any metric space is a contraction where every subset of k points has within an ck-’ factor of its maximal possible k l-dimensional volume. Feige invented these embeddings in devising a polylogarithmic approximation algorithm for the bandwidth problem using these embeddings. Feige’s methods have subsequently been used by Vempala for approximating versions of the VLSI layout problem. Feise showed that a (k, O(10,g~‘~ n,/m)) volume r&ecting embedding‘ eksted.” Be -recently found improved (k, 0( mdk log k + log n)) volume respecting embeddings. For metrics arising from planar graphs (planar metrics), we give (k,O(m)) volume respecting contractions. As a corollary, we give embeddings for Permission to makkr digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. XC’99 Miami Beach Florida Copyright ACM 1999 I-581 13-068-6/99/06...$5.00 planar metrics with distortion O(e). This gives rise to an O(e)-approximate max-flow min-cut theorem for multicommodity flow problems in planar graphs. We also give an improved bound for volume respecting embeddings for Euclidean metrics. In particular, we give an (k,O(dog klog D)) volume respecting embedding where D is the ratio of the largest distance to the smallest distance in the metric. Our results give improvements for Feige’s and Vempala’s approximation algorithms for planar and Euclidean metrics. For volume respecting embeddings, our embeddings do not degrade very fast when preserving the volumes of large subsets. This may be useful in the future for approximation algorithms or if volume .respecting embeddings prove to be of independent interest.
11142529
Segmentation of hybrid motions via hybrid quadratic surface analysis
In this paper, we investigate the mathematical problem underlying segmentation of hybrid motions: given a series of tracked feature correspondences between two (perspective) images, we seek to segment and estimate multiple motions, possibly of different types (e.g., affine, epipolar, and homography). In order to accomplish this task, we cast the problem into a more general mathematical framework of segmenting data samples drawn from a mixture of linear subspaces and quadratic surfaces. The result is a novel algorithm called hybrid quadratic surface analysis (HQSA). HQSA uses both the derivatives and Hessians of fitting polynomials for the data to separate linear data samples from quadratic data samples. These derivatives and Hessians also lead to important necessary conditions, based on the so-called mutual contraction subspace, to separate data samples on different quadratic surfaces. The algebraic solution we derive is non-iterative and numerically stable. It tolerates moderate noise and can be used in conjunction with outlier removal techniques. We show how to solve the hybrid motion segmentation problem using HQSA, and demonstrate its performance on simulated data with noise and on real perspective images.
7179412
Considering Priority in Overlay Multicast Protocols Under Heterogeneous Environments
Hosts participating in overlay multicast applications have a wide range of heterogeneity in bandwidth and participation characteristics. In this paper, we highlight and show the need to systematically consider prioritization as a key criterion in the design of protocols for overlay multicast. We identify trade-offs in the design of prioritization heuristics in two important contexts. The first part of the paper considers prioritization strategies in the context of heterogeneity in node outgoing bandwidth and node stay time durations, and a lack of correlation between the two dimensions. The second part of the paper considers bandwidth allocation and prioritization policies with multi-tree data delivery in environments with heterogeneity in outgoing bandwidth and a certain degree of altruistic behavior. We conduct a systematic study of the trade-offs using both real trace data, and sensitivity studies using synthetic workloads. To the best of our knowledge, this is the first work to identify and study these trade-offs, and to demonstrate the potential benefits of the resulting prioritization heuristics.
346423
Enabling contribution awareness in an overlay broadcasting system
We consider the design of bandwidth-demanding broadcasting applications using overlays in environments characterized by hosts with limited and asymmetric bandwidth, and significant heterogeneity in outgoing bandwidth. Such environments are critical to consider to extend the applicability of overlay multicast to mainstream Internet environments where insufficient bandwidth exists to support all hosts, but have not received adequate attention from the research community. We leverage the multi-tree framework and design heuristics to enable it to consider host contribution and operate in bandwidth-scarce environments. Our extensions seek to simultaneously achieve good utilization of system resources, performance to hosts commensurate to their contributions, and consistent performance. We have implemented the system and conducted an Internet evaluation on Planet-Lab using real traces from previous operational deployments of an overlay broadcasting system. Our results indicate for these traces, our heuristics can improve the performance of high contributors by 10-240% and facilitate equitable bandwidth distribution among hosts with similar contributions.
8131766
Segmentation of a piece-wise planar scene from perspective images
We study and compare two novel embedding methods for segmenting feature points of piece-wise planar structures from two (uncalibrated) perspective images. We show that a set of different homographies can be embedded in different ways to a higher-dimensional real or complex space, so that each homography corresponds to either a complex bilinear form or a real quadratic form. Each embedding reveals different algebraic properties and relations of homographies. We give a closed-form segmentation solution for each case by utilizing these properties based on subspace-segmentation methods. These theoretical results show that one can intrinsically segment a piece-wise planar scene from 2-D images without explicitly performing any 3-D reconstruction. The resulting segmentation may make subsequent 3-D reconstruction much better-conditioned. We demonstrate the proposed methods with some convincing experimental results.
504793
A case for end system multicast (keynote address)
The conventional wisdom has been that IP is the natural protocol layer for implementing multicast related functionality. However, ten years after its initial proposal, IP Multicast is still plagued with concerns pertaining to scalability, network management, deployment and support for higher layer functionality such as error, flow and congestion control. In this paper, we explore an alternative architecture for small and sparse groups, where end systems implement all multicast related functionality including membership management and packet replication. We call such a scheme End System Multicast. This shifting of multicast support from routers to end systems has the potential to address most problems associated with IP Multicast. However, the key concern is the performance penalty associated with such a model. In particular, End System Multicast introduces duplicate packets on physical links and incurs larger end-to-end delay than IP Multicast. In this paper, we study this question in the context of the Narada protocol. In Narada, end systems self-organize into an overlay structure using a fully distributed protocol. In addition, Narada attempts to optimize the efficiency of the overlay based on end-to-end measurements. We present details of Narada and evaluate it using both simulation and Internet experiments. Preliminary results are encouraging. In most simulations and Internet experiments, the delay and bandwidth penalty are low. We believe the potential benefits of repartitioning multicast functionality between end systems and routers significantly outweigh the performance penalty incurred.