A fast method for sorting data in a distributed data processing system is disclosed. Each processor P1 12i locally sorts its data into a local sorted file Si 34i, simultaneously producing an index to the sorted data and a file of key data records R' 32 each comprising a key value paired with the processor's identifier. Each processor produces a distribution table DTi 28i of its key values using the index, and sends the table to acoordinator processor 18 which merges the processors' tables into a global distribution table GST 30. The global distribution table assigns subranges of key values to the processors, and is broadcast back to them. Each processor then sends each paired key value and processor identifier to the processor assigned by the global distribution table to handle the subrange containing that key value. The processors receive and merge the incoming key data records simultaneously as they send such pairs to other processors. An output stream Vi 36i consisting only of processor identifiers is created by each processor from the merged key value and processor identifier pairs, and is sent to the host H 16, which merges it into a global output stream of processor identifiers. The processors simultaneously send their local sorted files Si to the host, which reads records from them in the order specified by the global output stream V.

Method for sorting using approximate key distribution in a distributed system

The main contribution of this work is to present elegant broadcast-efficient protocols for permutation routing, ranking, and sorting on single-hop Mobile Radio Networks with p stations and k radio channels, denoted by MRN(p,k). Clearly, any protocol performing these tasks on n items must perform /sup n///sub k/ broadcast rounds because each item must be broadcast at least once. We begin by presenting an optimal off-line permutation routing protocol using /sup n///sub k/ broadcast rounds for arbitrary k, p, and n. Further, we show that optimal on-line routing can be performed in /sup n///sub k/ broadcast rounds, provided that either k=1 or p=n. We then go on to develop an online routing protocol that takes 2/sup n///sub k/+k-1 broadcast rounds on the MRN(p,k), whenever k/spl les//spl radic//sup p///sub 2/. Using these routing protocols as basic building blocks, we develop a ranking protocol that takes 2/sup n///sub k/+o(/sup n///sub k/) broadcast rounds as well as a sorting protocol that takes 3/sup n///sub k/+o(/sup n///sub k/) broadcast rounds, provided that k /spl epsiv/ o(/spl radic/n) and p=n. Finally, we develop a ranking protocol that takes 3/sup n///sub k/+o(/sup n///sub k/) broadcast rounds, as well as a sorting protocol that takes 4/sup n///sub k/+o(/sup n///sub k/) broadcast rounds on the MRN(p,k), provided that k/spl les//spl radic//sup p///sub 2/ and p /spl epsiv/ o(n). Featuring very low proportionality constants, our protocols offer a vast improvement over the state of the art.

Broadcast-efficient protocols for mobile radio networks

Some common guidelines that can be used to design parallel algorithms under the single-channel broadcast communication model are presented. Several graph problems are solved, including topological ordering, the connected component problem, breadth-first search, and depth-first search. If an ideal conflict resolution scheme is used, all of the algorithms require O(n) time by using n processors. Under such a situation, the algorithms are all optimal. If a realistic conflict resolution is used, the algorithms require O(n log n) time by using n/log n processors. For both cases, all of the algorithms achieve optimal speedups. >

Parallel graph algorithms based upon broadcast communications

We present an asynchronous distributed algorithm to determine an ear decomposition of an arbitrary, connected, bidirectional network containing n-nodes and m-links which uses O(m) messages and which can be completed in O(n) time. Using the ear decomposition, we obtain the following results for a distributed network: 1) The distributed ear decomposition algorithm can be used to test biconnectivity, determine biconnected components, find cutpoints and bridges using O(m) messages in O(n) time. 2) The distributed ear decomposition algorithm can be used to test if a biconnected network is outerplanar using O(n) messages in O(n) time, and if the network is outerplanar, the embedding is also given using the same message and time complexity.

An optimal distributed ear decomposition algorithm with applications to biconnectivity and outerplanarity testing

In this paper, we shall first propose an optimal conflict-free parallel sorting algorithm under the single-channel broadcast communication model. The time complexity of this algorithm is O((n/p)log(n/p)+n) if p processors are used to sort n data elements. We then apply our single-channel sorting algorithm to improve the multi-channel sorting algorithm proposed by Marberg and Gafni. Since there is a constraint for the Marberg and Gafni's algorithm, we shall propose another conflict-free multi-channel sorting algorithm without this constraint. The time complexity of this algorithm is O((n/p)log(n/p)+(n/k)log2k) if there are n data elements to be sorted by using p processors with k channels.

/pdf/conflict-free-sorting-algorithms-under-single-channel-and-3wzhzdy1zj.pdf

Conflict-Free Sorting Algorithms Under Single-Channel and Multi-Channel Broadcast Communication Models

A straight-line-topology local area network (LAN) to which a number of nodes are connected either in series or in parallel is considered. A file F is arbitrarily partitioned among these sites. The problem studied is that of rearranging the records of the file such that the keys of records at lower-ranking sites are all smaller than those at higher-ranking sites. Lower bounds on the worst-case communication complexity are given for both the series and parallel arrangements, and algorithms optimal for all networks and files are presented. >

Distributed sorting on local area networks

The problem of recognizing whether a given network is a tree, ring, star, complete graph, or bipartite graph is considered. Unified algorithms to recognize if the network is any one of the above are presented in each of three classes of algorithms-with centralized, decentralized, and noncentralized initiations. It is shown that the communication and time complexities of the centralized algorithm are linear in e and d, respectively, while those for decentralized algorithm are O(e+n log n) and O(n), respectively (e is the number of edges, n is the number of processors, and d is the diameter of the graph). The complexities for noncentralized algorithms are, respectively O(e+n log k), where k is the level number, and O(n). >

K.V.S. Ramarao

Papers

Distributed sorting on local area networks

Distributed algorithms for network recognition problems