Results 1  10
of
57
Approximate distance oracles
 J. ACM
"... Let G = (V, E) be an undirected weighted graph with V  = n and E  = m. Let k ≥ 1 be an integer. We show that G = (V, E) can be preprocessed in O(kmn 1/k) expected time, constructing a data structure of size O(kn 1+1/k), such that any subsequent distance query can be answered, approximately, in ..."
Abstract

Cited by 210 (8 self)
 Add to MetaCart
Let G = (V, E) be an undirected weighted graph with V  = n and E  = m. Let k ≥ 1 be an integer. We show that G = (V, E) can be preprocessed in O(kmn 1/k) expected time, constructing a data structure of size O(kn 1+1/k), such that any subsequent distance query can be answered, approximately, in O(k) time. The approximate distance returned is of stretch at most 2k − 1, i.e., the quotient obtained by dividing the estimated distance by the actual distance lies between 1 and 2k−1. A 1963 girth conjecture of Erdős, implies that Ω(n 1+1/k) space is needed in the worst case for any real stretch strictly smaller than 2k + 1. The space requirement of our algorithm is, therefore, essentially optimal. The most impressive feature of our data structure is its constant query time, hence the name “oracle”. Previously, data structures that used only O(n 1+1/k) space had a query time of Ω(n 1/k). Our algorithms are extremely simple and easy to implement efficiently. They also provide faster constructions of sparse spanners of weighted graphs, and improved tree covers and distance labelings of weighted or unweighted graphs. 1
Concurrent Online Tracking of Mobile Users
 J. ACM
, 1991
"... This paper deals with the problem of maintaining a distributed directory server, that enables us to keep track of mobile users in a distributed network in the presence of concurrent requests. The paper uses the graphtheoretic concept of regional matching for implementing efficient tracking mechanis ..."
Abstract

Cited by 207 (7 self)
 Add to MetaCart
This paper deals with the problem of maintaining a distributed directory server, that enables us to keep track of mobile users in a distributed network in the presence of concurrent requests. The paper uses the graphtheoretic concept of regional matching for implementing efficient tracking mechanisms. The communication overhead of our tracking mechanism is within a polylogarithmic factor of the lower bound. 1 Introduction Since the primary function of a communication network is to provide communication facilities between users and processes in the system, one of the key problems such a network faces is the need to be able to Department of Mathematics and Lab. for Computer Science, M.I.T., Cambridge, MA 02139, USA. Email: baruch@theory.lcs.mit.edu. Supported by Air Force Contract TNDGAFOSR860078, ARO contract DAAL0386K0171, NSF contract CCR8611442, DARPA contract N0001489J 1988, and a special grant from IBM. y Departmentof Applied Mathematicsand Computer Science, The Weizm...
Compact routing schemes
 in SPAA ’01: Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
"... We describe several compact routing schemes for general weighted undirected networks. Our schemes are simple and easy to implement. The routing tables stored at the nodes of the network are all very small. The headers attached to the routed messages, including the name of the destination, are extrem ..."
Abstract

Cited by 196 (7 self)
 Add to MetaCart
We describe several compact routing schemes for general weighted undirected networks. Our schemes are simple and easy to implement. The routing tables stored at the nodes of the network are all very small. The headers attached to the routed messages, including the name of the destination, are extremely short. The routing decision at each node takes constant time. Yet, the stretch of these routing schemes, i.e., the worst ratio between the cost of the path on which a packet is routed and the cost of the cheapest path from source to destination, is a small constant. Our schemes achieve a nearoptimal tradeoff between the size of the routing tables used and the resulting stretch. More specifically, we obtain: 1. A routing scheme that uses only ~ O(n 1=2) bits of memory at each node of an nnode network that has stretch 3. The space is optimal, up to logarithmic factors, in the sense that
Distributed Object Location in a Dynamic Network
, 2004
"... Modern networking applications replicate data and services widely, leading to a need for locationindependent routingthe ability to route queries to objects using names independent of the objects' physical locations. Two important properties of such a routing infrastructure are routing locality a ..."
Abstract

Cited by 167 (16 self)
 Add to MetaCart
Modern networking applications replicate data and services widely, leading to a need for locationindependent routingthe ability to route queries to objects using names independent of the objects' physical locations. Two important properties of such 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 nearestneighbor problem for these networks. We describe our solution in the context of Tapestry, an overlay network infrastructure that employs techniques proposed by Plaxton et al. [24].
Excluded Minors, Network Decomposition, and Multicommodity Flow
, 1993
"... In this paper we show that, given a graph and parameters ffi and r, we can find either a Kr;r minor or an edgecut of size O(mr=ffi) whose removal yields components of weak diameter O(r 2 ffi); i.e., every pair of nodes in such a component are at distance O(r 2 ffi) in the original graph. Usi ..."
Abstract

Cited by 108 (6 self)
 Add to MetaCart
In this paper we show that, given a graph and parameters ffi and r, we can find either a Kr;r minor or an edgecut of size O(mr=ffi) whose removal yields components of weak diameter O(r 2 ffi); i.e., every pair of nodes in such a component are at distance O(r 2 ffi) in the original graph. Using this lemma, we improve the best known bounds for the mincut maxflow ratio for multicommodity flows in graphs with forbidden small minors. In general graphs, it was known that the ratio is O(log k) for the uniformdemand case (the case where there is a unitdemand commodity between every pair of nodes), and that the ratio is O(log 2 k) for arbitrary demands, where k is the number of commodities. In this paper we show that for graphs excluding any fixed graph as a minor (e.g. planar graphs or boundedgenus graphs), the ratio is O(1) for the uniformdemand case and O(log k) for the arbitrary demand case. For such graphs, our method yields minratio cut approximation algorithms wit...
Competitive Distributed File Allocation
, 1993
"... This paper deals with the file allocation problem [BFR92] concerning the dynamic optimization of communication costs to access data in a distributed environment. We develop a dynamic file reallocation strategy that adapts online to a sequence of read and write requests whose location and relative ..."
Abstract

Cited by 105 (12 self)
 Add to MetaCart
This paper deals with the file allocation problem [BFR92] concerning the dynamic optimization of communication costs to access data in a distributed environment. We develop a dynamic file reallocation strategy that adapts online to a sequence of read and write requests whose location and relative frequencies are completely unpredictable. This is achieved by replicating the file in response to read requests and migrating the file in response to write requests while paying the associated communications costs, so as to be closer to processors that access it frequently. We develop first explicit deterministic online strategy assuming existence of global information about the state of the network; previous (deterministic) solutions were complicated and more expensive. Our solution has (optimal) logarithmic competitive ratio. The paper also contains the first explicit deterministic data migration [BS89] algorithm achieving the best known competitive ratio for this problem. Using somewhat ...
Gem: graph embedding for routing and datacentric storage in sensor networks without geographic information
, 2003
"... Information ..."
Compact and Localized Distributed Data Structures
 JOURNAL OF DISTRIBUTED COMPUTING
, 2001
"... This survey concerns the role of data structures for compactly storing and representing various types of information in a localized and distributed fashion. Traditional approaches to data representation are based on global data structures, which require access to the entire structure even if the sou ..."
Abstract

Cited by 72 (25 self)
 Add to MetaCart
This survey concerns the role of data structures for compactly storing and representing various types of information in a localized and distributed fashion. Traditional approaches to data representation are based on global data structures, which require access to the entire structure even if the sought information involves only a small and local set of entities. In contrast, localized data representation schemes are based on breaking the information into small local pieces, or labels, selected in a way that allows one to infer information regarding a small set of entities directly from their labels, without using any additional (global) information. The survey focuses on combinatorial and algorithmic techniques, and covers complexity results on various applications, including compact localized schemes for message routing in communication networks, and adjacency and distance labeling schemes.
Bypassing the embedding: Algorithms for lowdimensional metrics
 In Proceedings of the 36th ACM Symposium on the Theory of Computing (STOC
, 2004
"... The doubling dimension of a metric is the smallest k such that any ball of radius 2r can be covered using 2 k balls of radius r. This concept for abstract metrics has been proposed as a natural analog to the dimension of a Euclidean space. If we could embed metrics with low doubling dimension into l ..."
Abstract

Cited by 65 (4 self)
 Add to MetaCart
The doubling dimension of a metric is the smallest k such that any ball of radius 2r can be covered using 2 k balls of radius r. This concept for abstract metrics has been proposed as a natural analog to the dimension of a Euclidean space. If we could embed metrics with low doubling dimension into low dimensional Euclidean spaces, they would inherit several algorithmic and structural properties of the Euclidean spaces. Unfortunately however, such a restriction on dimension does not suffice to guarantee embeddibility in a normed space. In this paper we explore the option of bypassing the embedding. In particular we show the following for low dimensional metrics: • Quasipolynomial time (1+ɛ)approximation algorithm for various optimization problems such as TSP, kmedian and facility location. • (1 + ɛ)approximate distance labeling scheme with optimal label length. • (1+ɛ)stretch polylogarithmic storage routing scheme.
Routing in networks with low doubling dimension
 In 26 th International Conference on Distributed Computing Systems (ICDCS). IEEE Computer
, 2006
"... This paper studies compact routing schemes for networks with low doubling dimension. Two variants are explored, nameindependent routing and labeled routing. The key results obtained for this model are the following. First, we provide the first nameindependent solution. Specifically, we achieve con ..."
Abstract

Cited by 63 (8 self)
 Add to MetaCart
This paper studies compact routing schemes for networks with low doubling dimension. Two variants are explored, nameindependent routing and labeled routing. The key results obtained for this model are the following. First, we provide the first nameindependent solution. Specifically, we achieve constant stretch and polylogarithmic storage. Second, we obtain the first truly scalefree solutions, namely, the network’s aspect ratio is not a factor in the stretch. Scalefree schemes are given for three problem models: nameindependent routing on graphs, labeled routing on metric spaces, and labeled routing on graphs. Third, we prove a lower bound requiring linear storage for stretch < 3 schemes. This has the important ramification of separating for the first time the nameindependent problem model from the labeled model for these networks, since compact stretch1+ε labeled schemes are known to be possible.