There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Expression.- Spectral Clustering Gene Ontology Terms to Group Genes by Function.- Dynamic De-Novo Prediction of microRNAs Associated with Cell Conditions: A Search Pruned by Expression.- Clustering Gene Expression Series with Prior Knowledge.- A Linear Time Biclustering Algorithm for Time Series Gene Expression Data.- Time-Window Analysis of Developmental Gene Expression Data with Multiple Genetic Backgrounds.- Phylogeny.- A Lookahead Branch-and-Bound Algorithm for the Maximum Quartet Consistency Problem.- Computing the Quartet Distance Between Trees of Arbitrary Degree.- Using Semi-definite Programming to Enhance Supertree Resolvability.- An Efficient Reduction from Constrained to Unconstrained Maximum Agreement Subtree.- Pattern Identification in Biogeography.- On the Complexity of Several Haplotyping Problems.- A Hidden Markov Technique for Haplotype Reconstruction.- Algorithms for Imperfect Phylogeny Haplotyping (IPPH) with a Single Homoplasy or Recombination Event.- Networks.- A Faster Algorithm for Detecting Network Motifs.- Reaction Motifs in Metabolic Networks.- Reconstructing Metabolic Networks Using Interval Analysis.- Genome Rearrangements.- A 1.375-Approximation Algorithm for Sorting by Transpositions.- A New Tight Upper Bound on the Transposition Distance.- Perfect Sorting by Reversals Is Not Always Difficult.- Minimum Recombination Histories by Branch and Bound.- Sequences.- A Unifying Framework for Seed Sensitivity and Its Application to Subset Seeds.- Generalized Planted (l,d)-Motif Problem with Negative Set.- Alignment of Tandem Repeats with Excision, Duplication, Substitution and Indels (EDSI).- The Peres-Shields Order Estimator for Fixed and Variable Length Markov Models with Applications to DNA Sequence Similarity.- Multiple Structural RNA Alignment with Lagrangian Relaxation.- Faster Algorithms for Optimal Multiple Sequence Alignment Based on Pairwise Comparisons.- Ortholog Clustering on a Multipartite Graph.- Linear Time Algorithm for Parsing RNA Secondary Structure.- A Compressed Format for Collections of Phylogenetic Trees and Improved Consensus Performance.- Structure.- Optimal Protein Threading by Cost-Splitting.- Efficient Parameterized Algorithm for Biopolymer Structure-Sequence Alignment.- Rotamer-Pair Energy Calculations Using a Trie Data Structure.- Improved Maintenance of Molecular Surfaces Using Dynamic Graph Connectivity.- The Main Structural Regularities of the Sandwich Proteins.- Discovery of Protein Substructures in EM Maps.

Algorithms in Bioinformatics: 5th International Workshop, WABI 2005, Mallorca, Spain, October 3-6, 2005, Proceedings (Lecture Notes in Computer Science / Lecture Notes in Bioinformatics)

Computational geometry.

Time-Efficient Maze Routing Algorithms on Reconfigurable Mesh Architectures

Lowest common ancestors in trees and directed acyclic graphs

The transitive closure problem in O(1) time is solved by a new method that is far different from the conventional solution method. On processor arrays with reconfigurable bus systems, two O(1) time algorithms are proposed for computing the transitive closure of an undirected graph. One is designed on a three-dimensional n*n*n processor array with a reconfigurable bus system, and the other is designed on a two-dimensional n/sup 2/*n/sup 2/ processor array with a reconfigurable bus system, where n is the number of vertices in the graph. Using the O(1) time transitive closure algorithms, many other graph problems are solved in O(1) time. These problems include recognizing bipartite graphs and finding connected components, articulation points, biconnected components, bridges, and minimum spanning trees in undirected graphs. >

Constant time algorithms for the transitive closure and some related graph problems on processor arrays with reconfigurable bus systems

A Cartesian product network is obtained by applying the cross operation on two graphs. We study the problem of constructing the maximum number of edge-disjoint spanning trees (abbreviated to EDSTs) in Cartesian product networks. Let G=(V/sub G/, E/sub G/) be a graph having n/sub 1/ EDSTs and F=(V/sub F/, E/sub F/) be a graph having n/sub 2/ EDSTs. Two methods are proposed for constructing EDSTs in the Cartesian product of G and F, denoted by G/spl times/F. The graph G has t/sub 1/=|E/sub G/|/spl middot/n/sub 1/(|V/sub G/|-1) more edges than that are necessary for constructing n/sub 1/ EDSTs in it, and the graph F has t2=|E/sub F/'-n/sub 2/(|V/sub F/|-1) more edges than that are necessary for constructing n/sub 2/ EDSTs in it. By assuming that t/sub 1//spl ges/n/sub 1/ and t/sub 2//spl ges/n/sub 2/, our first construction shows that n/sub 1/+n/sub 2/ EDSTS can be constructed in G/spl times/F. Our second construction does not need any assumption and it constructs n/sub 1/+n/sub 2/-1 EDSTs in G/spl times/F. By applying the proposed methods, it is easy to construct the maximum numbers of EDSTs in many important Cartesian product networks, such as hypercubes, tori, generalized hypercubes, mesh connected trees, and hyper Petersen networks.

Biing-Feng Wang

Papers

Constant time algorithms for the transitive closure and some related graph problems on processor arrays with reconfigurable bus systems

Constructing edge-disjoint spanning trees in product networks

Two-dimensional processor array with a reconfigurable bus system is at least as powerful as CRCW model

Linear time algorithms for the ring loading problem with demand splitting

Efficient Parallel Algorithms for Optimally Locating a Path and a Tree of a Specified Length in a Weighted Tree Network