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.
125992802
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.
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.
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].
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.
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.
27336833
An Efficient Distributed Algorithm for Finding Virtual Backbones in Wireless Ad-Hoc Networks
A minimum connected dominating set is an efficient approach to form a virtual backbone for ad-hoc networks. We propose a tree based distributed time/message efficient approximation algorithm to compute a small connected dominating set without using geographic positions. The algorithm has O(n) time, O(n log n) message complexity, and has an approximation factor of eight. The algorithm is implemented using dominating set simulation program, which shows that our method gives smaller connected dominating set than the existing methods.
5596998
Computing Refined Buneman Trees in Cubic Time
Reconstructing the evolutionary tree for a set of n species based on pairwise distances between the species is a fundamental problem in bioinformatics. Neighbor joining is a popular distance based tree reconstruction method. It always proposes fully resolved binary trees despite missing evidence in the underlying distance data. Distance based methods based on the theory of Buneman trees and refined Buneman trees avoid this problem by only proposing evolutionary trees whose edges satisfy a number of constraints. These trees might not be fully resolved but there is strong combinatorial evidence for each proposed edge. The currently best algorithm for computing the refined Buneman tree from a given distance measure has a running time of O(n 5) and a space consumption of O(n 4). In this paper, we present an algorithm with running time O(n 3) and space consumption O(n 2). The improved complexity of our algorithm makes the method of refined Buneman trees computational competitive to methods based on neighbor joining.
42405939
Prediction of Bead Geometry in Pulsed Current Gas Tungsten Arc Welding of Aluminum Using Artificial Neural Networks
15441480
Fast techniques for the optimal smoothing of stored video
Abstract. Work-ahead smoothing is a technique whereby a server, transmitting stored compressed video to a client, utilizes client buffer space to reduce the rate variability of the transmitted stream. The technique requires the server to compute a schedule of transfer under the constraints that the client buffer neither overflows nor underflows. Recent work established an optimal off-line algorithm (which minimizes peak, variance and rate variability of the transmitted stream) under the assumptions of fixed client buffer size, known worst case network jitter, and strict playback of the client video. In this paper, we examine the practical considerations of heterogeneous and dynamically variable client buffer sizes, variable worst case network jitter estimates, and client interactivity. These conditions require on-line computation of the optimal transfer schedule. We focus on techniques for reducing on-line computation time. Specifically, (i) we present an algorithm for precomputing and storing the optimal schedules for all possible client buffer sizes in a compact manner; (ii) we show that it is theoretically possible to precompute and store compactly the optimal schedules for all possible estimates of worst case network jitter; (iii) in the context of playback resumption after client interactivity, we show convergence of the recomputed schedule with the original schedule, implying greatly reduced on-line computation time; and (iv) we propose and empirically evaluate an “approximation scheme” that produces a schedule close to optimal but takes much less computation time.