The Integration of Task and Data Parallel Skeletons

We describe a skeletal parallel programming library which integrates task and data parallel constructs within an API for C++. Traditional skeletal requirements for higher orderness and polymorphism are achieved through exploitation of operator overloading and templates, while the underlying parallelism is provided by MPI. We present a case study describing two algorithms for the travelling salesman problem

Towards Generic Scalable Parallel Combinatorial Search

Combinatorial search problems in mathematics, e.g. in finite geometry, are notoriously hard; a state-of-the-art backtracking search algorithm can easily take months to solve a single problem. There is clearly demand for parallel combinatorial search algorithms scaling to hundreds of cores and beyond. However, backtracking combinatorial searches are challenging to parallelise due to their sensitivity to search order and due to the their irregularly shaped search trees. Moreover, scaling parallel search to hundreds of cores generally requires highly specialist parallel programming expertise. This paper proposes a generic scalable framework for solving hard combinatorial problems. Key elements are distributed memory task parallelism (to achieve scale), work stealing (to cope with irregularity), and generic algorithmic skeletons for combinatorial search (to reduce the parallelism expertise required). We outline two implementations: a mature Haskell Tree Search Library (HTSL) based around algorithmic skeletons and a prototype C++ Tree Search Library (CTSL) that uses hand coded applications. Experiments on maximum clique problems and on a problem in finite geometry, the search for spreads in H(4,2^2), show that (1) CTSL consistently outperforms HTSL on sequential runs, and (2) both libraries scale to 200 cores, e.g. speeding up spreads search by a factor of 81 (HTSL) and 60 (CTSL), respectively. This demonstrates the potential of our generic framework for scaling parallel combinatorial search to large distributed memory platforms

Replicable parallel branch and bound search

Combinatorial branch and bound searches are a common technique for solving global optimisation and decision problems. Their performance often depends on good search order heuristics, refined over decades of algorithms research. Parallel search necessarily deviates from the sequential search order, sometimes dramatically and unpredictably, e.g. by distributing work at random. This can disrupt effective search order heuristics and lead to unexpected and highly variable parallel performance. The variability makes it hard to reason about the parallel performance of combinatorial searches. This paper presents a generic parallel branch and bound skeleton, implemented in Haskell, with replicable parallel performance. The skeleton aims to preserve the search order heuristic by distributing work in an ordered fashion, closely following the sequential search order. We demonstrate the generality of the approach by applying the skeleton to 40 instances of three combinatorial problems: Maximum Clique, 0/1 Knapsack and Travelling Salesperson. The overheads of our Haskell skeleton are reasonable: giving slowdown factors of between 1.9 and 6.2 compared with a class-leading, dedicated, and highly optimised C++ Maximum Clique solver. We demonstrate scaling up to 200 cores of a Beowulf cluster, achieving speedups of 100x for several Maximum Clique instances. We demonstrate low variance of parallel performance across all instances of the three combinatorial problems and at all scales up to 200 cores, with median Relative Standard Deviation (RSD) below 2%. Parallel solvers that do not follow the sequential search order exhibit far higher variance, with median RSD exceeding 85% for Knapsack

The Münster Skeleton Library ‚Muesli‘:A Comprehensive Overview

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On Designing Multicore-aware Simulators for Biological Systems

The stochastic simulation of biological systems is an increasingly popular technique in bioinformatics. It often is an enlightening technique, which may however result in being computational expensive. We discuss the main opportunities to speed it up on multi-core platforms, which pose new challenges for parallelisation techniques. These opportunities are developed in two general families of solutions involving both the single simulation and a bulk of independent simulations (either replicas of derived from parameter sweep). Proposed solutions are tested on the parallelisation of the CWC simulator (Calculus of Wrapped Compartments) that is carried out according to proposed solutions by way of the FastFlow programming framework making possible fast development and efficient execution on multi-cores.Comment: 19 pages + cover pag

A Breezing Proof of the KMW Bound

In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW) proved a hardness result for several fundamental graph problems in the LOCAL model: For any (randomized) algorithm, there are input graphs with $n$ nodes and maximum degree $\Delta$ on which $\Omega(\min\{\sqrt{\log n/\log \log n},\log \Delta/\log \log \Delta\})$ (expected) communication rounds are required to obtain polylogarithmic approximations to a minimum vertex cover, minimum dominating set, or maximum matching. Via reduction, this hardness extends to symmetry breaking tasks like finding maximal independent sets or maximal matchings. Today, more than $15$ years later, there is still no proof of this result that is easy on the reader. Setting out to change this, in this work, we provide a fully self-contained and $\mathit{simple}$ proof of the KMW lower bound. The key argument is algorithmic, and it relies on an invariant that can be readily verified from the generation rules of the lower bound graphs.Comment: 21 pages, 6 figure