A Generic Framework for Engineering Graph Canonization Algorithms

The state-of-the-art tools for practical graph canonization are all based on the individualization-refinement paradigm, and their difference is primarily in the choice of heuristics they include and in the actual tool implementation. It is thus not possible to make a direct comparison of how individual algorithmic ideas affect the performance on different graph classes. We present an algorithmic software framework that facilitates implementation of heuristics as independent extensions to a common core algorithm. It therefore becomes easy to perform a detailed comparison of the performance and behaviour of different algorithmic ideas. Implementations are provided of a range of algorithms for tree traversal, target cell selection, and node invariant, including choices from the literature and new variations. The framework readily supports extraction and visualization of detailed data from separate algorithm executions for subsequent analysis and development of new heuristics. Using collections of different graph classes we investigate the effect of varying the selections of heuristics, often revealing exactly which individual algorithmic choice is responsible for particularly good or bad performance. On several benchmark collections, including a newly proposed class of difficult instances, we additionally find that our implementation performs better than the current state-of-the-art tools

Group Communication Patterns for High Performance Computing in Scala

We developed a Functional object-oriented Parallel framework (FooPar) for high-level high-performance computing in Scala. Central to this framework are Distributed Memory Parallel Data structures (DPDs), i.e., collections of data distributed in a shared nothing system together with parallel operations on these data. In this paper, we first present FooPar's architecture and the idea of DPDs and group communications. Then, we show how DPDs can be implemented elegantly and efficiently in Scala based on the Traversable/Builder pattern, unifying Functional and Object-Oriented Programming. We prove the correctness and safety of one communication algorithm and show how specification testing (via ScalaCheck) can be used to bridge the gap between proof and implementation. Furthermore, we show that the group communication operations of FooPar outperform those of the MPJ Express open source MPI-bindings for Java, both asymptotically and empirically. FooPar has already been shown to be capable of achieving close-to-optimal performance for dense matrix-matrix multiplication via JNI. In this article, we present results on a parallel implementation of the Floyd-Warshall algorithm in FooPar, achieving more than 94 % efficiency compared to the serial version on a cluster using 100 cores for matrices of dimension 38000 x 38000

Inferring Chemical Reaction Patterns Using Rule Composition in Graph Grammars

Modeling molecules as undirected graphs and chemical reactions as graph rewriting operations is a natural and convenient approach tom odeling chemistry. Graph grammar rules are most naturally employed to model elementary reactions like merging, splitting, and isomerisation of molecules. It is often convenient, in particular in the analysis of larger systems, to summarize several subsequent reactions into a single composite chemical reaction. We use a generic approach for composing graph grammar rules to define a chemically useful rule compositions. We iteratively apply these rule compositions to elementary transformations in order to automatically infer complex transformation patterns. This is useful for instance to understand the net effect of complex catalytic cycles such as the Formose reaction. The automatically inferred graph grammar rule is a generic representative that also covers the overall reaction pattern of the Formose cycle, namely two carbonyl groups that can react with a bound glycolaldehyde to a second glycolaldehyde. Rule composition also can be used to study polymerization reactions as well as more complicated iterative reaction schemes. Terpenes and the polyketides, for instance, form two naturally occurring classes of compounds of utmost pharmaceutical interest that can be understood as "generalized polymers" consisting of five-carbon (isoprene) and two-carbon units, respectively

Fast Ant Colony Optimization on Runtime Reconfigurable Processor Arrays

Ant Colony Optimization (ACO) is a metaheuristic used to solve combinatorial optimization problems. As with other metaheuristics, like evolutionary methods, ACO algorithms often show good optimization behavior but are slow when compared to classical heuristics. Hence, there is a need to find fast implementations for ACO algorithms. In order to allow a fast parallel implementation, we propose several changes to a standard form of ACO algorithms. The main new features are the non-generational approach and the use of a threshold based decision function for the ants. We show that the new algorithm has a good optimization behavior and also allows a fast implementation on reconfigurable processor arrays. This is the first implementation of the ACO approach on a reconfigurable architecture. The running time of the algorithm is quasi-linear in the problem size n and the number of ants on a reconfigurable mesh with n2 processors, each provided with only a constant number of memory words

On solving permutation scheduling problems with ant colony optimization

A new approach for solving permutation scheduling problems with ant colony optimization (ACO) is proposed in this paper. The approach assumes that no precedence constraints between the jobs have to be fulfilled. It is tested with an ACO algorithm for the single-machine total weighted deviation problem. In the new approach the ants allocate the places in the schedule not sequentially, as in the standard approach, but in random order. This leads to a better utilization of the pheromone information. It is shown by experiments that adequate combinations between the standard approach which can profit from list scheduling heuristics and the new approach perform particularly well

On the Complexity of Reconstructing Chemical Reaction Networks

The analysis of the structure of chemical reaction networks is crucial for a better understanding of chemical processes. Such networks are well described as hypergraphs. However, due to the available methods, analyses regarding network properties are typically made on standard graphs derived from the full hypergraph description, e.g.\ on the so-called species and reaction graphs. However, a reconstruction of the underlying hypergraph from these graphs is not necessarily unique. In this paper, we address the problem of reconstructing a hypergraph from its species and reaction graph and show NP-completeness of the problem in its Boolean formulation. Furthermore we study the problem empirically on random and real world instances in order to investigate its computational limits in practice

Ant colony optimization for resource-constrained project scheduling

An ant colony optimization (ACO) approach for the resource-constrained project scheduling problem (RCPSP) is presented. Several new features that are interesting for ACO in general are proposed and evaluated. In particular, the use of a combination of two pheromone evaluation methods by the ants to find new solutions, a change of the influence of the heuristic on the decisions of the ants during the run of the algorithm, and the option that an elitist ant forgets the best-found solution are studied. We tested the ACO algorithm on a set of large benchmark problems from the Project Scheduling Library. Compared to several other heuristics for the RCPSP, including genetic algorithms, simulated annealing, tabu search, and different sampling methods, our algorithm performed best on average. For nearly one-third of all benchmark problems, which were not known to be solved optimally before, the algorithm was able to find new best solutions

A parameter-adaptive dynamic programming approach for inferring cophylogenies

Background Coevolutionary systems like hosts and their parasites are commonly used model systems for evolutionary studies. Inferring the coevolutionary history based on given phylogenies of both groups is often done by employing a set of possible types of events that happened during coevolution. Costs are assigned to the different types of events and a reconstruction of the common history with a minimal sum of event costs is sought. Results This paper introduces a new algorithm and a corresponding tool called CoRe-PA, that can be used to infer the common history of coevolutionary systems. The proposed method utilizes an event-based concept for reconciliation analyses where the possible events are cospeciations, sortings, duplications, and (host) switches. All known event-based approaches so far assign costs to each type of cophylogenetic events in order to find a cost-minimal reconstruction. CoRe-PA uses a new parameter-adaptive approach, i.e., no costs have to be assigned to the coevolutionary events in advance. Several biological coevolutionary systems that have already been studied intensely in literature are used to show the performance of CoRe-PA. Conclusion From a biological point of view reasonable cost values for event-based reconciliations can often be estimated only very roughly. CoRe-PA is very useful when it is difficult or impossible to assign exact cost values to different types of coevolutionary events in advance