Optimal communication algorithms on star graphs using spanning tree constructions

The class of problems that are linearly equivalent to Satisfiability or a uniform method for proving NP-completeness

Extensions to constraint dependency parsing for spoken language processing

The computational problem of parsing a sentence in a tree-adjoining language is investigated. An interesting relation is studied between this problem and the well-known computational problem of Boolean matrix multiplication: it is shown that any algorithm for the solution of the former problem can easily be converted into an algorithm for the solution of the latter problem. This result bears on at least two important computational issues. First, we realize that a straightforward method that improves the known upper bound for tree-adjoining grammar parsing is hard to find. Second, we understand which features of the tree-adjoining grammar parsing problem are responsible for the claimed difficulty.

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Tree-adjoining grammar parsing and boolean matrix multiplication

In this paper we present a general strategy for finding efficient permutation routes in parallel networks. Among the popular parallel networks to which the strategy applies are mesh networks, hypercube networks, hypercube-derivative networks, ring networks, and star networks. The routes produced are generally congestion-free and take a number of routing steps that is within a small constant factor of the diameter of the network. Our basic strategy is derived from an algorithm that finds (in polynomial time) efficient permutation routes for aproduct network, G×H, given efficient permutation routes forG andH. We investigate the use of this algorithm for routingmultiple permutations and extend its applicability to a wide class of graphs, including several families ofCayley graphs. Finally, we show that our approach can be used to find efficient permutation routes among the remaining live nodes infaulty networks.

A unified framework for off-line permutation routing in parallel networks

An optimal parallel recognition/parsing algorithm is presented for languages generated by tree adjoining grammars (TAGs), a grammatical system for natural language. TAGs are strictly more powerful than context-free grammars (CFGs), e.g., they can generate $\{a'' b'' c'' | n \geqq 0\}$, which is not context-free. However, serial parsing of TAGs is also slower, having time complexity $O(n^{6})$ for inputs of length n (as opposed to $O(n^{3})$ for CFGs). The parallel algorithm achieves optimal speedup: it runs in linear time on a five-dimensional array of $n^5$ processors. Moreover, the processors are finite-state; i.e., their function and size depends only on the underlying grammar and not on the length of the input.

An optimal linear-time parallel parser for tree adjoining languages

In designing algorithms for a specific parallel architecture, a programmer has to cope with topological and cardinality variations. Both these problems always increase the programmer's effort. However, an ideal shared memory abstract parallel model called the parallel random access machine (PRAM) [KRUS86, KRUS88] that avoids these problems and also simple-to-program has been proposed. Unfortunately, the PRAM does not seem to be realizable in the present or even foreseeable technologies. On the other hand, a packet routing technique can be employed to simulate the PRAM on a feasible parallel architecture without significant loss of efficiency. The problem of routing is also important due to its intrinsic significance in distributed processing and its important role in the simulations among parallel models. The routing problem is defined as follows: Given a specific network and a set of packets of information in which a packet is an (origin, destination) pair. To start with, the packets are placed on their origins, one per node. These packets must be routed in parallel to their own destinations such that at most one packet passes through any link of the network at any time and all packets arrive at their destinations as quickly as possible. We are interested in a special case of the general routing problem called permutation routing in which the destinations form some permutation of the origins. A routing algorithm is said to be oblivious if the path taken by each packet is only dependent on its source and destination. An oblivious routing strategy is preferable since it will lead to a simple control structure for the individual processing elements. Also oblivious routing algorithms can be used in a distributed environment. In this paper we are concerned with only oblivious routing strategies. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-89-35. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/710 GENERAL ROUTING ALGORITHMS FOR STAR GRAPHS Michael A. Palis, Sanguthevar Rajasekaran and David S. L. Wei MS-CIS-89-35 LlNC LAB 153 Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 19104

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General Routing Algorithms for Star Graphs

Massively parallel algorithms are described for parsing with Tree Adjoining Grammar (TAG), a formalism for describing natural language. Sequential parsing algorithms for TAGs run in time quadratic in the grammar size, which is impractical for the very large grammars currently being developed for natural language. This paper presents two parallel algorithms, one running in time nearly linear in the grammar size, and the other running in time logarithmic in the grammar size. Both parallel algorithms were implemented on a Connection Machine CM-2 and performance measurements were obtained for varying grammar sizes.

Massively Parallel Parsing Algorithms for Natural Language

This paper addresses the problem of scheduling parallel programs represented as directed acyclic task graphs for execution on distributed memory parallel architectures. Because of the high communication overhead in existing parallel machines, a crucial step in scheduling IS task Clustering, the process of coalescing fine grain tasks into single coarser ones so that the overall execution time is minimized. The task clustering probtem is NP-hard, even when the number of processors is unbounded and task duplication is allowed. A simple greedy algorithm is presented for this problem which, for a task graph with arbitrary grahularity, produces a schedule whose makespan is at most twice optimal. Indeed, the quality of the schedule improves as the granularity of the task graph becomes larger. For example, if the granularity is at least 1/2, the makespan of the schedule is at most 5/3 times optimal. For a task graph with n tasks and e inter-task communication constraints, the algorithm runs in O(n(n lg n + e)) time, which is n times faster than the currently best known algorithm for this problem. Similar algorithms are developed that produce: (1) optimal schedules for coarse grain graphs; (2) 2-optimal schedules for trees with no task duplication; and (3) optimal schedules for coarse grain trees with no task duplication. Index Terms-Program task graph, task granularity, task scheduling, distributed memory architectures, approximation algorithms.

David S. L. Wei

Papers

An optimal linear-time parallel parser for tree adjoining languages

General Routing Algorithms for Star Graphs

Massively Parallel Parsing Algorithms for Natural Language

lustering and Scheduling for Distributed emory Parallel Architectures