arXiv subjects

Paul Brown

Publications and source records attributed to Paul Brown.

3 recordsLinked to original sources

arXiv2020

Fast Generation of Unlabelled Free Trees using Weight Sequences

In this paper, we introduce a new representation for ordered trees, the weight sequence representation. We then use this to construct new representations for both rooted trees and free trees, namely the canonical weight sequence representation. We construct algorithms for generating the weight sequence representations for all rooted and free trees of order n, and then add a number of modifications to improve the efficiency of the algorithms. Python implementations of the algorithms incorporate further improvements by using generators to avoid having to store the long lists of trees returned by the recursive calls, as well as caching the lists for rooted trees of small order, thereby eliminating many of the recursive calls. We further show how the algorithm can be modifed to generate adjacency list and adjacency matrix representations for free trees. We compared the run-times of our Python implementation for generating free trees with the Python implementation of the well-known WROM algorithm taken from NetworkX. The implementation of our algorithm is over four times as fast as the implementation of the WROM algorithm. The run-times for generating adjacency lists and matrices are somewhat longer than those for weight sequences, but are still over three times as fast as the corresponding implementations of the WROM algorithm.

cs.DS↗

arXiv2020

Supercards, Sunshines and Caterpillar Graphs

The vertex-deleted subgraph G-v, obtained from the graph G by deleting the vertex v and all edges incident to v, is called a card of G. The deck of G is the multiset of its unlabelled cards. The number of common cards b(G,H) of G and H is the cardinality of the multiset intersection of the decks of G and H. A supercard G+ of G and H is a graph whose deck contains at least one card isomorphic to G and at least one card isomorphic to H. We show how maximum sets of common cards of G and H correspond to certain sets of permutations of the vertices of a supercard, which we call maximum saturating sets. We apply the theory of supercards and maximum saturating sets to the case when G is a sunshine graph and H is a caterpillar graph. We show that, for large enough n, there exists some maximum saturating set that contains at least b(G,H)-2 automorphisms of G+, and that this subset is always isomorphic to either a cyclic or dihedral group. We prove that b(G,H)<=2(n+1)/5 for large enough n, and that there exists a unique family of pairs of graphs that attain this bound. We further show that, in this case, the corresponding maximum saturating set is isomorphic to the dihedral group.

math.CO↗

arXiv2017

ArrayBridge: Interweaving declarative array processing with high-performance computing

Scientists are increasingly turning to datacenter-scale computers to produce and analyze massive arrays. Despite decades of database research that extols the virtues of declarative query processing, scientists still write, debug and parallelize imperative HPC kernels even for the most mundane queries. This impedance mismatch has been partly attributed to the cumbersome data loading process; in response, the database community has proposed in situ mechanisms to access data in scientific file formats. Scientists, however, desire more than a passive access method that reads arrays from files. This paper describes ArrayBridge, a bi-directional array view mechanism for scientific file formats, that aims to make declarative array manipulations interoperable with imperative file-centric analyses. Our prototype implementation of ArrayBridge uses HDF5 as the underlying array storage library and seamlessly integrates into the SciDB open-source array database system. In addition to fast querying over external array objects, ArrayBridge produces arrays in the HDF5 file format just as easily as it can read from it. ArrayBridge also supports time travel queries from imperative kernels through the unmodified HDF5 API, and automatically deduplicates between array versions for space efficiency. Our extensive performance evaluation in NERSC, a large-scale scientific computing facility, shows that ArrayBridge exhibits statistically indistinguishable performance and I/O scalability to the native SciDB storage engine.

cs.DB↗