Parallel Algorithms for Burrows-Wheeler Compression and Decompression

We present work-optimal PRAM algorithms for Burrows-Wheeler compression and decompression of strings over a constant alphabet. For a string of length n, the depth of the compression algorithm is O(log2 n), and the depth of the the corresponding decompression algorithm is O(log n). These appear to be the first polylogarithmic-time work-optimal parallel algorithms for any standard lossless compression scheme. The algorithms for the individual stages of compression and decompression may also be of independent interest: 1. a novel O(log n)-time, O(n)-work PRAM algorithm for Huffman decoding; 2. original insights into the stages of the BW compression and decompression problems, bringing out parallelism that was not readily apparent, allowing them to be mapped to elementary parallel routines that have O(log n)-time, O(n)-work solutions, such as: (i) prefix-sums problems with an appropriately-defined associative binary operator for several stages, and (ii) list ranking for the final stage of decompression.NSF grant CCF-081150

Optimality program in segment and string graphs

Planar graphs are known to allow subexponential algorithms running in time $2^{O(\sqrt n)}$ or $2^{O(\sqrt n \log n)}$ for most of the paradigmatic problems, while the brute-force time $2^{\Theta(n)}$ is very likely to be asymptotically best on general graphs. Intrigued by an algorithm packing curves in $2^{O(n^{2/3}\log n)}$ by Fox and Pach [SODA'11], we investigate which problems have subexponential algorithms on the intersection graphs of curves (string graphs) or segments (segment intersection graphs) and which problems have no such algorithms under the ETH (Exponential Time Hypothesis). Among our results, we show that, quite surprisingly, 3-Coloring can also be solved in time $2^{O(n^{2/3}\log^{O(1)}n)}$ on string graphs while an algorithm running in time $2^{o(n)}$ for 4-Coloring even on axis-parallel segments (of unbounded length) would disprove the ETH. For 4-Coloring of unit segments, we show a weaker ETH lower bound of $2^{o(n^{2/3})}$ which exploits the celebrated Erd\H{o}s-Szekeres theorem. The subexponential running time also carries over to Min Feedback Vertex Set but not to Min Dominating Set and Min Independent Dominating Set.Comment: 19 pages, 15 figure

A Parallel Algorithm for Exact Bayesian Structure Discovery in Bayesian Networks

Exact Bayesian structure discovery in Bayesian networks requires exponential time and space. Using dynamic programming (DP), the fastest known sequential algorithm computes the exact posterior probabilities of structural features in $O(2(d+1)n2^n)$ time and space, if the number of nodes (variables) in the Bayesian network is $n$ and the in-degree (the number of parents) per node is bounded by a constant $d$. Here we present a parallel algorithm capable of computing the exact posterior probabilities for all $n(n-1)$ edges with optimal parallel space efficiency and nearly optimal parallel time efficiency. That is, if $p=2^k$ processors are used, the run-time reduces to $O(5(d+1)n2^{n-k}+k(n-k)^d)$ and the space usage becomes $O(n2^{n-k})$ per processor. Our algorithm is based the observation that the subproblems in the sequential DP algorithm constitute a $n$-$D$ hypercube. We take a delicate way to coordinate the computation of correlated DP procedures such that large amount of data exchange is suppressed. Further, we develop parallel techniques for two variants of the well-known \emph{zeta transform}, which have applications outside the context of Bayesian networks. We demonstrate the capability of our algorithm on datasets with up to 33 variables and its scalability on up to 2048 processors. We apply our algorithm to a biological data set for discovering the yeast pheromone response pathways.Comment: 32 pages, 12 figure

Competent genetic-evolutionary optimization of water distribution systems

A genetic algorithm has been applied to the optimal design and rehabilitation of a water distribution system. Many of the previous applications have been limited to small water distribution systems, where the computer time used for solving the problem has been relatively small. In order to apply genetic and evolutionary optimization technique to a large-scale water distribution system, this paper employs one of competent genetic-evolutionary algorithms - a messy genetic algorithm to enhance the efficiency of an optimization procedure. A maximum flexibility is ensured by the formulation of a string and solution representation scheme, a fitness definition, and the integration of a well-developed hydraulic network solver that facilitate the application of a genetic algorithm to the optimization of a water distribution system. Two benchmark problems of water pipeline design and a real water distribution system are presented to demonstrate the application of the improved technique. The results obtained show that the number of the design trials required by the messy genetic algorithm is consistently fewer than the other genetic algorithms