Parallel branch and bound and anomalies

In this paper we present a classification of parallel branch and bound algorithms and investigate the anomalies which can occur during the execution of such algorithms. We develop sufficient conditions to prevent deceleration anomalies from degrading the performance. Such conditions were already known for some synchronous cases. It turns out that these conditions can be generalized to arbitrary cases. Finally we develop necessary conditions for acceleration anomalies to improve upon the performance

Parallel branch and bound on an MIMD system

In this paper we give a classification of parallel branch and bound algorithms and develop a class of asynchronous branch and bound algorithms for execution on an MIMD system. We develop sufficient conditions to prevent the anomalies that can occur due to the parallelism, the asynchronicity or the nondeter- minism, from degrading the performance of the algorithm. Such conditions were known already for the synchronous case. It turns out that these conditions are sufficient for asynchronous algorithms as well. We also investigate the consequences of nonhomogeneous processing elements in a parallel computer system. We introduce the notions of perfect parallel time and achieved efficiency to empirically measure the effects of parallelism, because the traditional notions of speedup and efficiency are not capable of fully characterizing the actual execution of an asyn-chronous parallel algorithm. Finally we present some computational results obtained for the symmetric traveling salesman problem

Greedy Graph Colouring is a Misleading Heuristic

State of the art maximum clique algorithms use a greedy graph colouring as a bound. We show that greedy graph colouring can be misleading, which has implications for parallel branch and bound

Multi-threading a state-of-the-art maximum clique algorithm

We present a threaded parallel adaptation of a state-of-the-art maximum clique algorithm for dense, computationally challenging graphs. We show that near-linear speedups are achievable in practice and that superlinear speedups are common. We include results for several previously unsolved benchmark problems

Building Merger Trees from Cosmological N-body Simulations

Although a fair amount of work has been devoted to growing Monte-Carlo merger trees which resemble those built from an N-body simulation, comparatively little effort has been invested in quantifying the caveats one necessarily encounters when one extracts trees directly from such a simulation. To somewhat revert the tide, this paper seeks to provide its reader with a comprehensive study of the problems one faces when following this route. The first step to building merger histories of dark matter haloes and their subhaloes is to identify these structures in each of the time outputs (snapshots) produced by the simulation. Even though we discuss a particular implementation of such an algorithm (called AdaptaHOP) in this paper, we believe that our results do not depend on the exact details of the implementation but extend to most if not all (sub)structure finders. We then highlight different ways to build merger histories from AdaptaHOP haloes and subhaloes, contrasting their various advantages and drawbacks. We find that the best approach to (sub)halo merging histories is through an analysis that goes back and forth between identification and tree building rather than one which conducts a straightforward sequential treatment of these two steps. This is rooted in the complexity of the merging trees which have to depict an inherently dynamical process from the partial temporal information contained in the collection of instantaneous snapshots available from the N-body simulation.Comment: 19 pages, 28 figure

Asynchronous parallel branch and bound and anomalies

The parallel execution of branch and bound algorithms can result in seemingly unreasonable speedups or slowdowns. Almost never the speedup is equal to the increase in computing power. For synchronous parallel branch and bound, these effects have been studiedd extensively. For asynchronous parallelizations, only little is known. In this paper, we derive sufficient conditions to guarantee that an asynchronous parallel branch and bound algorithm (with elimination by lower bound tests and dominance) will be at least as fast as its sequential counterpart. The technique used for obtaining the results seems to be more generally applicable. The essential observations are that, under certain conditions, the parallel algorithm will always work on at least one node, that is branched from by the sequential algorithm, and that the parallel algorithm, after elimination of all such nodes, is able to conclude that the optimal solution has been found. Finally, some of the theoretical results are brought into connection with a few practical experiments

A Parallel Branch and Bound Algorithm for the Maximum Labelled Clique Problem

The maximum labelled clique problem is a variant of the maximum clique problem where edges in the graph are given labels, and we are not allowed to use more than a certain number of distinct labels in a solution. We introduce a new branch-and-bound algorithm for the problem, and explain how it may be parallelised. We evaluate an implementation on a set of benchmark instances, and show that it is consistently faster than previously published results, sometimes by four or five orders of magnitude.Comment: Author-final version. Accepted to Optimization Letter

Computational experiments with an asynchronous parallel branch and bound algorithm

In this paper we present an asynchronous branch and bound algorithm for execution on an MIMD system, state sufficient conditions to prevent the parallelism from degrading the performance of this algorithm, and investigate the consequences of having the algorithm executed by nonhomogeneous processing elements. We introduce the notions of perfect parallel time and achieved efficiency to empirically measure the effects of parallelism, because the traditional notions of speedup and processor utilization are not adequate for fully characterizing the actual execution of an asynchronous parallel branch and bound algorithm. Finally we present some computational results obtained for the symmetric traveling salesman problem

List scheduling revisited

We consider the problem of scheduling n jobs on m identical parallel machines to minimize a regular cost function. The standard list scheduling algorithm converts a list into a feasible schedule by focusing on the job start times. We prove that list schedules are dominant for this type of problem. Furthermore, we prove that an alternative list scheduling algorithm, focusing on the completion times rather than the start times, yields also dominant list schedules for problems with sequence dependent setup times

B-LOG: A branch and bound methodology for the parallel execution of logic programs

We propose a computational methodology -"B-LOG"-, which offers the potential for an effective implementation of Logic Programming in a parallel computer. We also propose a weighting scheme to guide the search process through the graph and we apply the concepts of parallel "branch and bound" algorithms in order to perform a "best-first" search using an information theoretic bound. The concept of "session" is used to speed up the search process in a succession of similar queries. Within a session, we strongly modify the bounds in a local database, while bounds kept in a global database are weakly modified to provide a better initial condition for other sessions. We also propose an implementation scheme based on a database machine using "semantic paging", and the "B-LOG processor" based on a scoreboard driven controller