Finding an extremum in a network

Levitan, Steven P.; Foster, Caxton C.

doi:10.1145/1067649.801741

Cited by 24 publications

(10 citation statements)

References 3 publications

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“…Foster [9] can find the maximum or minimum of n given elements in an expected O(log n) rounds on a conflict broadcast version of RN (n, 1). In this paper we assume the conflict-free version of RN (p, k).…”

Section: The Algorithm Of Levitan Andmentioning

confidence: 99%

An Efficient Randomized Routing Protocol for Single-Hop Radio Networks

Rajasekaran

Sharma

Ammar

et al. 2010

2010 39th International Conference on Parallel Processing

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In this paper we study the important problems of message routing, sorting, and selection in a radio network. A radio network consists of stations where each station is a hand-held device. We consider a single-hop radio network. In a single-hop network it is assumed that each station is within the transmission range of every other station. Let RN (p, k) stand for a single-hop network that has p stations and k communication channels. The problems of sorting and selection have been studied on RN (p, k). For these problems it is assumed that there are n/p elements to start with at each station. At the end of sorting, the least n/p elements should be in the first station, the next smallest n/p elements should be in the second station, and so on. The best known prior algorithm for sorting takes 4 n k + o n k broadcast rounds on a RN (p, k). In this paper we present a randomized algorithm that takes only 3 n k + o n k broadcast rounds with high probability.For the selection problem, it is known that the maximum or minimum element can be found in O(log n) rounds on a RN (n, 1), provided broadcast conflicts can be resolved in O(1) time. The problem of general selection has not been addressed. In this paper we present a randomized selection algorithm that takes O p k rounds on a RN (p, k) with high probability. An important message routing problem that is considered in the literature is one where there are n/p packets originating from each station and there are n/p packets destined for each station. The best known routing algorithms take nearly 2n/k times slots. An important open question has been if there exist algorithms that take only close to n/k time slots. Note that a trivial lower bound for routing is n/k. The existence of such algorithms will be highly relevant especially in emergencies and timecritical situations. In this paper we answer this question by presenting a randomized algorithm that takes nearly n/k time slots with high probability.

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Section: The Algorithm Of Levitan Andmentioning

confidence: 99%

An Efficient Randomized Routing Protocol for Single-Hop Radio Networks

Rajasekaran

Sharma

Ammar

et al. 2010

2010 39th International Conference on Parallel Processing

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“…Various broadcast communication models have been quite popular with the distributed processing and networking community [6], [11], [20], [21], [24], [29]. In recent years, efficient protocols, both asynchronous and synchronous, for various computational problems on broadcast communication models, including packet radio networks, have been proposed in the literature.…”

Section: State Of the Artmentioning

confidence: 99%

“…While many of these results were not stated in the context of MRN's, it is not hard to adapt them for this latter model. In particular, Levitan [20] and Levitan and Foster [21] have shown that if somehow broadcast conflicts are resolved in constant time, then on an wxnY I the minimum and maximum of n items can be computed in O(log n) time. They have also shown that on the same platform, the task of sorting n items takes yn time, while the task of computing a minimum spanning tree of an n-vertex graph takes O(n log n) time.…”

Section: State Of the Artmentioning

confidence: 99%

Broadcast-efficient protocols for mobile radio networks

Nakano

Olariu

Schwing

1999

IEEE Trans. Parallel Distrib. Syst.

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“…Levitan and Foster [9] proposed a model of a parallel computer that implements the procedure of Figure 3 using lockstep synchronization and concurrent read and write. A PE is associated with each input in the candidate set C. To implement step 2, all ] C ] PEs concurrently write to a shared variable, tent-max.…”

Section: Algorithmsmentioning

confidence: 99%

“…The algorithm muxl may be regarded as the asynchronous counterpart of a synchronous parallel algorithm proposed by Levitan and Foster [9] (described in Section 2). Megiddo [13] and Frieze and Rudolph [2] have given a probabilistic parallel algorithm, which uses n PEs and Q(n) shared variables to compute the maximum in constant time with overwhelming probability.…”

Section: Introductionmentioning

confidence: 99%

Simple, efficient, asynchronous parallel algorithms for maximization

Greenberg

Lubachevsky

Odlyzko

1988

ACM Trans. Program. Lang. Syst.

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The problem of computing the maximum of n inputs on an asynchronous parallel computer is considered. In general, the inputs may arrive staggered in time, the number of processors available to the maximization algorithm may vary during its execution, and the number of inputs, n, may be initially unknown. Two simple, efficient algorithms to compute the maximum are presented. Each algorithm may be invoked asynchronously, as new inputs and processors arrive. Performance measures that account for the response times of the invocations are introduced, and the algorithms are analyzed under these measures.

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Finding an extremum in a network

Cited by 24 publications

References 3 publications

An Efficient Randomized Routing Protocol for Single-Hop Radio Networks

An Efficient Randomized Routing Protocol for Single-Hop Radio Networks

Broadcast-efficient protocols for mobile radio networks

Simple, efficient, asynchronous parallel algorithms for maximization

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