3,664 research outputs found
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
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
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
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
Partially ordered distributed computations on asynchronous point-to-point networks
Asynchronous executions of a distributed algorithm differ from each other due
to the nondeterminism in the order in which the messages exchanged are handled.
In many situations of interest, the asynchronous executions induced by
restricting nondeterminism are more efficient, in an application-specific
sense, than the others. In this work, we define partially ordered executions of
a distributed algorithm as the executions satisfying some restricted orders of
their actions in two different frameworks, those of the so-called event- and
pulse-driven computations. The aim of these restrictions is to characterize
asynchronous executions that are likely to be more efficient for some important
classes of applications. Also, an asynchronous algorithm that ensures the
occurrence of partially ordered executions is given for each case. Two of the
applications that we believe may benefit from the restricted nondeterminism are
backtrack search, in the event-driven case, and iterative algorithms for
systems of linear equations, in the pulse-driven case
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
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