Various heuristic algorithms to minimise the two-page crossing numbers of graphs

We propose several new heuristics for the twopage book crossing problem, which are based on recent algorithms for the corresponding one-page problem. Especially, the neural network model for edge allocation is combined for the first time with various one-page algorithms. We investigate the performance of the new heuristics by testing them on various benchmark test suites. It is found out that the new heuristics outperform the previously known heuristics and produce good approximations of the planar crossing number for severalwell-known graph families. We conjecture that the optimal two-page drawing of a graph represents the planar drawing of the graph

Experimental Evaluation of Book Drawing Algorithms

A $k$-page book drawing of a graph $G=(V,E)$ consists of a linear ordering of its vertices along a spine and an assignment of each edge to one of the $k$ pages, which are half-planes bounded by the spine. In a book drawing, two edges cross if and only if they are assigned to the same page and their vertices alternate along the spine. Crossing minimization in a $k$-page book drawing is NP-hard, yet book drawings have multiple applications in visualization and beyond. Therefore several heuristic book drawing algorithms exist, but there is no broader comparative study on their relative performance. In this paper, we propose a comprehensive benchmark set of challenging graph classes for book drawing algorithms and provide an extensive experimental study of the performance of existing book drawing algorithms.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Genetic algorithms for the 2-page book drawing problem of graphs

The minimisation of edge crossings in a book drawing of a graph is one of the important goals for a linear VLSI design, and the 2-page crossing number of a graph provides an upper bound for the standard planar crossing number. We design genetic algorithms for the 2-page drawings, and test them on the benchmark test suits, Rome graphs and Random Connected Graphs. We also test some circulant graphs, and get better results than previously presented in the literature. Moreover, we formalise three conjectures for certain kinds of circulant graphs, supported by our experimental results

Heuristic crossing minimisation algorithms for the two-page drawing problem

The minimisation of edge crossings in a book drawing of a graph G is one of the important goals for a linear VLSI design, and the two-page crossing number of a graph G provides an upper bound for the standard planar crossing number. We propose several new heuristics for the two-page drawing problem, and test them on benchmark test suites, Rome graphs and Random Connected Graphs. We also test some typical graphs, and get some exact results. The results for some circulant graphs are better than the one presented by Cimikowski. We have a conjecture for cartesian graphs, supported by our experimental results, and provide direct methods to get optimal solutions for 3- or 4-row meshes and Halin graphs

Parallelisation of genetic algorithms for the 2-page crossing number problem

Genetic algorithms have been applied to solve the 2-page crossing number problem successfully, but since they work with one global population, the search time and space are limited. Parallelisation provides an attractive prospect to improve the efficiency and solution quality of genetic algorithms. This paper investigates the complexity of parallel genetic algorithms (PGAs) based on two evaluation measures: Computation-time to Communication-time and Population-size to Chromosomesize. Moreover, the paper unifies the framework of PGA models with the function PGA (subpopulation size; cluster size, migration period; topology), and explores the performance of PGAs for the 2-page crossing number problem

Reinforcement Learning for Racecar Control

This thesis investigates the use of reinforcement learning to learn to drive a racecar in the simulated environment of the Robot Automobile Racing Simulator. Real-life race driving is known to be difficult for humans, and expert human drivers use complex sequences of actions. There are a large number of variables, some of which change stochastically and all of which may affect the outcome. This makes driving a promising domain for testing and developing Machine Learning techniques that have the potential to be robust enough to work in the real world. Therefore the principles of the algorithms from this work may be applicable to a range of problems. The investigation starts by finding a suitable data structure to represent the information learnt. This is tested using supervised learning. Reinforcement learning is added and roughly tuned, and the supervised learning is then removed. A simple tabular representation is found satisfactory, and this avoids difficulties with more complex methods and allows the investigation to concentrate on the essentials of learning. Various reward sources are tested and a combination of three are found to produce the best performance. Exploration of the problem space is investigated. Results show exploration is essential but controlling how much is done is also important. It turns out the learning episodes need to be very long and because of this the task needs to be treated as continuous by using discounting to limit the size of the variables stored. Eligibility traces are used with success to make the learning more efficient. The tabular representation is made more compact by hashing and more accurate by using smaller buckets. This slows the learning but produces better driving. The improvement given by a rough form of generalisation indicates the replacement of the tabular method by a function approximator is warranted. These results show reinforcement learning can work within the Robot Automobile Racing Simulator, and lay the foundations for building a more efficient and competitive agent

Various island-based parallel genetic algorithms for the 2-page drawing problem

Genetic algorithms have been applied to solve the 2-page drawing problem successfully, but they work with one global population, so the search time and space are limited. Parallelization provides an attractive prospect in improving the efficiency and solution quality of genetic algorithms. One of the most popular tools for parallel computing is Message Passing Interface (MPI). In this paper, we present four island models of Parallel Genetic Algorithms with MPI: island models with linear, grid, random graph topologies, and island model with periodical synchronisation. We compare their efficiency and quality of solutions for the 2-page drawing problem on a variety of graphs

Solutions to decision-making problems in management engineering using molecular computational algorithms and experimentations

制度:新 ; 報告番号:甲3368号 ; 学位の種類:博士(工学) ; 授与年月日:2011/5/23 ; 早大学位記番号:新568

Loom: Query-aware Partitioning of Online Graphs

As with general graph processing systems, partitioning data over a cluster of machines improves the scalability of graph database management systems. However, these systems will incur additional network cost during the execution of a query workload, due to inter-partition traversals. Workload-agnostic partitioning algorithms typically minimise the likelihood of any edge crossing partition boundaries. However, these partitioners are sub-optimal with respect to many workloads, especially queries, which may require more frequent traversal of specific subsets of inter-partition edges. Furthermore, they largely unsuited to operating incrementally on dynamic, growing graphs. We present a new graph partitioning algorithm, Loom, that operates on a stream of graph updates and continuously allocates the new vertices and edges to partitions, taking into account a query workload of graph pattern expressions along with their relative frequencies. First we capture the most common patterns of edge traversals which occur when executing queries. We then compare sub-graphs, which present themselves incrementally in the graph update stream, against these common patterns. Finally we attempt to allocate each match to single partitions, reducing the number of inter-partition edges within frequently traversed sub-graphs and improving average query performance. Loom is extensively evaluated over several large test graphs with realistic query workloads and various orderings of the graph updates. We demonstrate that, given a workload, our prototype produces partitionings of significantly better quality than existing streaming graph partitioning algorithms Fennel and LDG