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55
Multiple Communication in MultiHop Radio Networks
 SIAM Journal on Computing
, 1993
"... Two tasks of communication in a multihop synchronous radio network are considered: pointtopoint communication and broadcast (sending a message to all nodes of a network). Efficient protocols for both problems are presented. Even though the protocols are probabilistic, it is shown how to acknowled ..."
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Cited by 69 (1 self)
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Two tasks of communication in a multihop synchronous radio network are considered: pointtopoint communication and broadcast (sending a message to all nodes of a network). Efficient protocols for both problems are presented. Even though the protocols are probabilistic, it is shown how to acknowledge messages deterministically. Let n, D, and Δ be the number of nodes, the diameter and the maximum degree of our network, respectively. Both protocols require a setup phase in which a BFS tree is constructed. This phase takes O ((n + Dlogn)logΔ) time. After the setup, k pointtopoint transmissions require O ((k +D)logΔ) time on the average. Therefore the network allows a new transmission every O (logΔ) time slots. Also, k broadcasts require an average of O ((k +D)logΔlogn) time. Hence the average throughput of the network is a broadcast every O(logΔlogn) time slots. Both protocols pipeline the messages along the BFS tree. They are always successful on the graph spanned by the BFS tree. Their probabilistic behavior refers only to the running time. Using the above protocols the ranking problem is solved in O (nlognlogΔ) time. The performance analysis of both protocols constitutes a new application of queueing theory.
Parallel Ear Decomposition Search (EDS) And STNumbering In Graphs
, 1986
"... [LEC67] linear time serial algorithm for testing planarity of graphs uses the linear time serial algorithm of [ET76] for stnumbering. This stnumbering algorithm is based on depthfirst search (DFS). A known conjecture states that DFS, which is a key technique in designing serial algorithms, is n ..."
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Cited by 42 (2 self)
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[LEC67] linear time serial algorithm for testing planarity of graphs uses the linear time serial algorithm of [ET76] for stnumbering. This stnumbering algorithm is based on depthfirst search (DFS). A known conjecture states that DFS, which is a key technique in designing serial algorithms, is not amenable to polylog time parallelism using "around linearly" (or even polynomially) many processors. The first contribution of this paper is a general method for searching efficiently in parallel undirected graphs, called eardecomposition search (EDS). The second contribution demonstrates the applicability of this search method. We present an efficient parallel algorithm for stnumbering in a biconnected graph. The algorithm runs in logarithmic time using a linear number of processors on a concurrentread concurrentwrite (CRCW) PRAM. An efficient parallel algorithm for the problem did not exist before. The problem was not even known to be in NC. 1. Introduction We define the problems ...
SubLinear Distributed Algorithms for Sparse Certificates and Biconnected Components.
, 1995
"... A certificate for the k connectivity y of a graph G = (V; E) is a subset E 0 of E such that (V; E 0 ) is k connected iff G is k connected. Let n = jV j and m = jEj. A certificate is called sparse if it has size O(kn). We present a distributed algorithm for computing sparse certificate for k co ..."
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Cited by 16 (1 self)
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A certificate for the k connectivity y of a graph G = (V; E) is a subset E 0 of E such that (V; E 0 ) is k connected iff G is k connected. Let n = jV j and m = jEj. A certificate is called sparse if it has size O(kn). We present a distributed algorithm for computing sparse certificate for k connectivity whose time complexity is O(k(D+n 0:614 )) where D is the diameter of the network. A new algorithm for identifying biconnected components is also presented. This algorithm is significantly simpler than many existing algorithms and can be implemented in a distributed environment to run in O(D+n 0:614 ) time. Both algorithms improve on the previous best known time bounds. Our main focus in this paper is the time complexity. However, no more than a polynomial number of messages, each of size O(log n), are generated by the algorithm. 1 Introduction Connectivity is an important property of graphs with many applications in computer science. We study the distributed time complexity o...
Disjoint multipath routing using colored trees
 Elsevier COMNET
, 2005
"... Abstract — Multipath routing (MPR) is an effective strategy to achieve robustness, load balancing, congestion reduction, and increased throughput in computer networks. Disjoint multipath routing (DMPR) requires the multiple paths to be link or nodedisjoint. Both MPR and DMPR poses significant chal ..."
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Cited by 14 (5 self)
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Abstract — Multipath routing (MPR) is an effective strategy to achieve robustness, load balancing, congestion reduction, and increased throughput in computer networks. Disjoint multipath routing (DMPR) requires the multiple paths to be link or nodedisjoint. Both MPR and DMPR poses significant challenges in terms of obtaining loopfree multiple (disjoint) paths and effectively forwarding the data over the multiple paths, the latter being particularly significant in IP datagram networks. This paper develops a twodisjoint multipath routing strategy using colored trees. Two trees, red and blue, that are rooted at a designated node called the drain are formed. The paths from a given source to the drain on the two trees are link or nodedisjoint. Such an approach requires every node to maintain only two preferred neighbors for each destination, one on each tree. This paper (1) formulates the problem of coloredtrees construction as an integer linear program (ILP); and (2) develops the first distributed algorithm to construct the colored trees using only local information. We demonstrate the effectiveness of the distributed algorithm by evaluating it on grid and random topologies and comparing to the optimal obtained by solving the ILP. I.
Qualityofservice and qualityofprotection issues in preplanned recovery schemes using redundant trees
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATION
, 2003
"... In this paper, we study qualityofservice (QoS) and qualityofprotection (QoP) issues in redundant tree based preplanned recovery schemes for a singlelink failure in twoedge connected graphs and for a singlenode failure in twoconnected graphs. We present schemes (to be called GMFBG schemes) ..."
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Cited by 13 (0 self)
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In this paper, we study qualityofservice (QoS) and qualityofprotection (QoP) issues in redundant tree based preplanned recovery schemes for a singlelink failure in twoedge connected graphs and for a singlenode failure in twoconnected graphs. We present schemes (to be called GMFBG schemes) that generalize the schemes (to be called MFBG schemes) developed by Médard et al. to construct a pair of redundant trees, called red and blue trees, which guarantees fast recovery from any singlelink/node failure, as long as the failed node is not the root node. Using the GMFBG schemes, we study QoS issues relating to red/blue trees. We present effective heuristics for computing a pair of redundant trees with low average delay or small total cost. We develop an optimal algorithm for computing a pair of red/blue trees with maximum bandwidth. Furthermore, a pair of red/blue trees guarantees fast recovery from simultaneous multiple failures if it satisfies certain properties. This leads us to define the concept of QoP of a pair of red/blue trees. We present an effective heuristic to construct a pair of red/blue trees with high QoP. The paper concludes with a discussion of computational results that demonstrate the effectiveness of the different algorithms presented.
OutputSensitive Reporting of Disjoint Paths
, 1996
"... A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. For ..."
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Cited by 11 (2 self)
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A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. For k < 3, we present an optimal data structure for G that uses O(n) space and executes kpath queries in outputsensitive O() time. For triconnected planar graphs, our results make use of a new combinatorial structure that plays the same role as bipolar (st) orientations for biconnected planar graphs. This combinatorial structure also yields an alternative construction of convex grid drawings of triconnected planar graphs.
Directed st Numberings, Rubber Bands, and Testing Digraph kVertex Connectivity
"... Let G = (V, E) be a directed graph and n denote V. We show that G is kvertex connected iff for every subset X of V with IX I = k, there is an embedding of G in the (k I)dimensional space Rkl, ~ : V ~Rkl, such that no hyperplane contains k points of {~(v) \ v G V}, and for each v E V – X, f( ..."
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Cited by 10 (2 self)
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Let G = (V, E) be a directed graph and n denote V. We show that G is kvertex connected iff for every subset X of V with IX I = k, there is an embedding of G in the (k I)dimensional space Rkl, ~ : V ~Rkl, such that no hyperplane contains k points of {~(v) \ v G V}, and for each v E V – X, f(v) is in the convex hull of {~(w) I (v, W) G E}. This result generalizes to directed graphs the notion of convex embedding of undirected graphs introduced by Linial, LOV6SZ and Wigderson in ‘Rubber bands, convex embedding and graph connectivity, ” Combinatorics 8 (1988), 91102. Using this characterization, a directed graph can be tested for kvertex connectivity by a Monte Carlo algorithm in time O((M(n) + nkf(k)). (log n)) with error probability < l/n, and by a Las Vegas algorithm in expected time O((lf(n)+nM(k)).k), where M(n) denotes the number of arithmetic steps for multiplying two n x n matrices (Al(n) = 0(n2.3755)). Our Monte Carlo algorithm improves on the best previous deterministic and randomized time complexities for k> no. *9; e.g., for k = @, the factor of improvement is> n0.G2. Both algorithms have processor efficient parallel versions that run in O((log n)2) time on the EREW PRAM model of computation, using a number of processors equal to (logn) times the respective sequential time complexities. Our Monte Carlo parallel algorithm improves on the number of processors used by the best previous (Monte Carlo) parallel algorithm by a factor of at least (n2/(log n)3) while having the same running time. Generalizing the notion of st numberings, we give a combinatorial construction of a directed st nulmberiug for any 2vertex connected directed graph.
Efficient computation of implicit representations of sparse graphs
 Discrete Applied Mathematics
, 1997
"... The problem of finding an implicit representation for a graph such that vertex adjacency can be tested quickly is fundamental to all graph algorithms. In particular, it is possible to represent sparse graphs on n vertices using O(n) space such that vertex adjacency is tested in O(1) time. We show he ..."
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Cited by 10 (0 self)
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The problem of finding an implicit representation for a graph such that vertex adjacency can be tested quickly is fundamental to all graph algorithms. In particular, it is possible to represent sparse graphs on n vertices using O(n) space such that vertex adjacency is tested in O(1) time. We show here how to construct such a representation efficiently by providing simple and optimal algorithms, both in a sequential and a parallel setting. Our sequential algorithm runs in O(n) time. The parallel algorithm runs in O(log n) time using O(n=log n) CRCW PRAM processors, or in O(log n log n) time using O(n = log n log
Linear time construction of redundant trees for recovery schemes enhancing qop and qos
 IN PROCEEDINGS OF IEEE INFOCOM
, 2005
"... ... elegant recovery scheme (known as the MFBG scheme) using redundant trees. Xue, Chen and Thulasiraman extended the MFBG scheme and introduced the concept of quality of protection (QoP) as a metric of multifailure recovery capabilities for single failure recovery schemes. In this paper, we present ..."
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Cited by 10 (0 self)
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... elegant recovery scheme (known as the MFBG scheme) using redundant trees. Xue, Chen and Thulasiraman extended the MFBG scheme and introduced the concept of quality of protection (QoP) as a metric of multifailure recovery capabilities for single failure recovery schemes. In this paper, we present three linear time algorithms for constructing redundant trees for single link failure recovery in 2edge connected graphs and for single node failure recovery in 2connected graphs. Our first algorithm aims at high QoP for single link recovery schemes in 2edge connected graphs. The previous best algorithm has a running time of O(n 2 (m + n)), wherenand m are the number of nodes and links in the network. Our algorithm has a running time of O(m + n), with comparable performance. Our second algorithm aims at high QoS for single link recovery schemes in 2edge connected graphs. Our algorithm improves the previous best algorithm with O(n 2 (m + n)) time complexity to O(m + n) time complexity with comparable performance. Our third algorithm aims at high QoS for single node recovery schemes in 2connected graphs. Again, our algorithm improves the previous best algorithm with O(n 2 (m + n)) time complexity to O(m + n) time complexity with comparable performance. Simulation results show that our new algorithms outperform previously known linear time algorithms significantly in terms of QoP or QoS, and outperform other known algorithms in terms of running time, with comparable QoP of QoS performance.
Random Sampling and Greedy Sparsification for Matroid Optimization Problems.
 Mathematical Programming
, 1998
"... Random sampling is a powerful tool for gathering information about a group by considering only a small part of it. We discuss some broadly applicable paradigms for using random sampling in combinatorial optimization, and demonstrate the effectiveness of these paradigms for two optimization problems ..."
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Cited by 9 (2 self)
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Random sampling is a powerful tool for gathering information about a group by considering only a small part of it. We discuss some broadly applicable paradigms for using random sampling in combinatorial optimization, and demonstrate the effectiveness of these paradigms for two optimization problems on matroids: finding an optimum matroid basis and packing disjoint matroid bases. Applications of these ideas to the graphic matroid led to fast algorithms for minimum spanning trees and minimum cuts. An optimum matroid basis is typically found by a greedy algorithm that grows an independent set into an the optimum basis one element at a time. This continuous change in the independent set can make it hard to perform the independence tests needed by the greedy algorithm. We simplify matters by using sampling to reduce the problem of finding an optimum matroid basis to the problem of verifying that a given fixed basis is optimum, showing that the two problems can be solved in roughly the same ...