Parallel Processing Letters

We show that for hypergraphs of bounded edge size, the problem of extending a given list of maximal independent sets is NC-reducible to the computation of an arbitrary maximal independent set for an induced sub-hypergraph. The latter problem is known to be in RNC. In particular, our reduction yields an incremental RNC dualization algorithm for hypergraphs of bounded edge size, a problem previously known to be solvable in polynomial incremental time. We also give a similar parallel algorithm for the dualization problem on the product of arbitrary lattices which have a bounded number of immediate predecessors for each element.

In this paper, we present an algorithm that builds optimal schedules for complete in-trees on two uniform processors, with arbitrary integer speed ratios, in the presence of communication delays.

The problem of sorting an intransitive total ordered set, a generalization of regular sorting, is considered. This generalized sorting is based on the fact that there exists a special linear ordering (also called a generalized sorted sequence) for any intransitive total ordered set, or equivalently, the existence of a Hamiltonian path in a tournament. A new data structure called semi-heap is proposed to construct an optimal Θ(n log n) sorting algorithm. We also provide a cost-optimal parallel algorithm using semi-heap. The run time of this algorithm is Θ(n) with Θ(log n) processors under the EREW PRAM model. The use of a Hamiltonian path (generalized sorting sequence) as an approximation of a ranking system in a tournament is also discussed.

Deadlock prevention is usually realized by forbidding transmissions that could eventually cause a deadlock to occur. However, an optimal routing algorithm with respect to channel utilization forbids transmissions only when they would bring the network into a configuration that will necessarily evolve into a deadlock. Hence, optimal deadlock prevention is closely related to deadlock prediction. In this paper it is shown that wormhole deadlock and livelock prediction is a hard problem for both oblivious and adaptive routing.

We address the problem of allocating optical bandwidth to a set of communication requests in a tree-shaped all-optical network that utilizes Wavelength Division Multiplexing (WDM) technology. WDM technology establishes communication between pairs of nodes of the network by establishing tranceiver–receiver paths and assigning wavelengths to each path so that no two paths going through the same link use the same wavelength. Optical bandwidth is the number of distinct wavelengths. The important engineering problem to be solved is to establish communication between pairs of nodes so that the total number of wavelengths used is minimized.

In this paper, we focus on a special case of the problem considering patterns of requests that are symmetric, i.e. for any transmitter–receiver pair of nodes (v₁, v₂) there also exists its symmetric (v₂, v₁). Our motivation lies in the fact that many services that are expected to be supported by high performance optical networks in the future, require bidirectional reservation of bandwidth. We prove that the problem of optimizing the number of wavelengths used is NP-hard even when the underlying network is a binary tree. We also present two interesting lower bounds.

Dictionary compression belongs to the class of lossless compression methods and is mainly used for compressing text files. The most known examples of this technique are the algorithms of the LZ coding family whose common feature is the use of an adaptive dictionary which is dynamically adjusting during the algorithm execution. In this paper, we present a parallel algorithm for one of these coding algorithms, namely the LZ77 coding algorithm also known as a sliding-window coding algorithm. We also present a parallel algorithm for the corresponding LZ77 decoding algorithm. Although there exist PRAM algorithms for various dictionary compression methods, their rather irregular structure has discouraged their implementation on practical interconnection networks such as the mesh and hypercube. However in the case of LZ77 coding/decoding, we show how to exploit the specific properties of the algorithm in order to achieve an efficient implementation on the hypercube. Specifically, we show how to encode a N-character string on a N-node hypercube in only O(log²N) time. In contrast, a naive simulation of a PRAM algorithm of the LZ77 coding on the hypercube would have O(log³N) complexity. In addition, we further enhance the performance of our parallel algorithms by using some known heuristics from the field of text compression.

In this paper, an algorithm is presented to embedd a ring in an n-dimensional hypercube with at most n-1 faults; subsequently, the embedded ring is used for efficient deadlock-free multicast routing between all the fault-free nodes. Simulation results are presented to compare the performance of the algorithm to that of the routing algorithm proposed in [9] for a fault-free hypercube to study the performance degradation because of faults. A modification to the algorithm of [9] is also presented for improved performance.

In this paper we analyze the computational power of random geometric networks in the presence of random (edge or node) faults considering several important network parameters. We first analyze how to emulate an original random geometric network G on a faulty network F. Our results state that, under the presence of some natural assumptions, random geometric networks can tolerate a constant node failure probability with a constant slowdown. In the case of constant edge failure probability the slowdown is an arbitrarily small constant times the logarithm of the graph order. Then we consider several network measures, stated as linear layout problems (Bisection, Minimum Linear Arrangement and Minimum Cut Width). Our results show that random geometric networks can tolerate a constant edge (or node) failure probability while maintaining the order of magnitude of the measures considered here. Finally we show that, with high probability, random geometric networks with (edge or node) faults do have a Hamiltonian cycle, provided the failure probability is constant. Such capability enables performing distributed computations based on end-to-end communication protocols.

Programming with parallel skeletons is an attractive framework because it encourages programmers to develop efficient and portable parallel programs. However, extracting parallelism from sequential specifications and constructing efficient parallel programs using the skeletons are still difficult tasks. In this paper, we propose an analytical approach to transforming recursive functions on general recursive data structures into compositions of parallel skeletons. Using static slicing, we have defined a classification of subexpressions based on their data-parallelism. Then, skeleton-based parallel programs are generated from the classification. To extend the scope of parallelization, we have adopted more general parallel skeletons which do not require the associativity of argument functions. In this way, our analytical method can parallelize recursive functions with complex data flows.

In this paper, we propose the design and development of a fault tolerant and recovery scheme for the Message Passing Interface (MPI). The proposed scheme consists of a detection mechanism for detecting process failures, and a recovery mechanism. Two different cases are considered, both assuming the existence of a monitoring process, the Observer which triggers the recovery procedure in case of failure. In the first case, each process keeps a buffer with its own message traffic to be used in case of failure, while the implementor uses periodical tests for notification of failure by the Observer. The recovery function simulates all the communication of the processes with the dead one by re-sending to the replacement process all the messages destined for the dead one. In the second case, the Observer receives and stores all message traffic, and sends to the replacement all the buffered messages destined for the dead process. Solutions are provided to the dead communicator problem caused by the death of a process. A description of the prototype developed is provided along with the results of the experiments performed for efficiency and performance.

We consider the problem of establishing gravity in cellular automata. In particular, when cellular automata states can be partitioned into empty, particle, and wall types, with the latter enclosing rectangular areas, we desire rules that will make the particles fall down and pile up on the bottom of each such area. We desire the rules to be both simple and time-efficient. We propose a block rule, and prove that it piles up particles on a grid of height h in time at most 3*h.