3724518
Long Cycles through a Linear Forest
For a graph G and an integer k?1, let S(G)={x?V(G):dG(x)=0} and ?k(G)=min{?ki=1dG(vi):{v1, v2, ?, vk} is an independent set of G}. The main result of this paper is as follows. Let k?3, m?0, and 0?s?k?3. Let G be a (m+k?1)-connected graph and let F be a subgraph of G with |E(F)|=m and |S(F)|=s. If every component of F is a path, then G has a cycle of length ?min{|V(G)|, 2k?k(G)?m} passing through E(F)?V(F). This generalizes three related results known previously.
29782824
Hamilton connectivity of line graphs and claw-free graphs
205878836
A generalization of fan's condition and forbidden subgraph conditions for hamiltonicity
Abstract Let G be a 2-connected graph with n vertices and H be an induced subgraph of G. Denote V0 ≔ {v ϵ V(G): d(v) ⩾ n/2}. If there exists a pair of vertices x and y at distance 2 in H such that {x, y} ⊆ V(H)βV0, then H is called degree light. Let F be the unique graph with degree sequence (1, 1, 1, 3, 3, 3). In this paper, we prove that if G contains no degree light K1, 3 and every degree light F of G contains no induced P4 of G − V0, then G is hamiltonian.
14260384
Perfect Circular Arc Coloring
The circular arc coloring problem is to find a minimum coloring of a set of arcs of a circle so that no two overlapping arcs share a color. This NP-hard problem arises in a rich variety of applications and has been studied extensively. In this paper we present an O(n2m) combinatorial algorithm for optimally coloring any set of arcs that corresponds to a perfect graph, and propose a new approach to the general circular arc coloring problem.
38894685
A Strongly Polynomial Algorithm for the Inverse Shortest Arborescence Problem
Abstract In this paper an inverse problem of the weighted shortest arborescence problem is discussed. That is, given a directed graph G and a set of nonnegative costs on its arcs, we need to modify those costs as little as possible to ensure that T, a given v1 -arborescence of G, is the shortest one. It is found that only the cost of T needs modifying. An O(n3) combinatorial algorithm is then proposed. This algorithm also gives an optimal solution to the inverse weighted shortest path problem.
17504195
Parallel skeletons for manipulating general trees
Trees are important datatypes that are often used in representing structured data such as XML. Though trees are widely used in sequential programming, it is hard to write efficient parallel programs manipulating trees, because of their irregular and ill-balanced structures. In this paper, we propose a solution based on the skeletal approach. We formalize a set of skeletons (abstracted computational patterns) for rose trees (general trees of arbitrary shapes) based on the theory of Constructive Algorithmics. Our skeletons for rose trees are extensions of those proposed for lists and binary trees. We show that we can implement the skeletons efficiently in parallel, by combining the parallel binary-tree skeletons for which efficient parallel implementations are already known. As far as we are aware, we are the first who have formalized and implemented a set of simple but expressive parallel skeletons for rose trees.
18834097
Utilization of two sample t-test statistics from redundant probe sets to evaluate different probe set algorithms in GeneChip studies
BackgroundThe choice of probe set algorithms for expression summary in a GeneChip study has a great impact on subsequent gene expression data analysis. Spiked-in cRNAs with known concentration are often used to assess the relative performance of probe set algorithms. Given the fact that the spiked-in cRNAs do not represent endogenously expressed genes in experiments, it becomes increasingly important to have methods to study whether a particular probe set algorithm is more appropriate for a specific dataset, without using such external reference data.ResultsWe propose the use of the probe set redundancy feature for evaluating the performance of probe set algorithms, and have presented three approaches for analyzing data variance and result bias using two sample t-test statistics from redundant probe sets. These approaches are as follows: 1) analyzing redundant probe set variance based on t-statistic rank order, 2) computing correlation of t-statistics between redundant probe sets, and 3) analyzing the co-occurrence of replicate redundant probe sets representing differentially expressed genes. We applied these approaches to expression summary data generated from three datasets utilizing individual probe set algorithms of MAS5.0, dChip, or RMA. We also utilized combinations of options from the three probe set algorithms. We found that results from the three approaches were similar within each individual expression summary dataset, and were also in good agreement with previously reported findings by others. We also demonstrate the validity of our findings by independent experimental methods.ConclusionAll three proposed approaches allowed us to assess the performance of probe set algorithms using the probe set redundancy feature. The analyses of redundant probe set variance based on t-statistic rank order and correlation of t-statistics between redundant probe sets provide useful tools for data variance analysis, and the co-occurrence of replicate redundant probe sets representing differentially expressed genes allows estimation of result bias. The results also suggest that individual probe set algorithms have dataset-specific performance.
5453797
List Homomorphism with Accumulation
This paper introduces accumulation into list homomorphisms for systematic development of both efficient and correct parallel programs. New parallelizable recursive pattern called H-homomorphism is given, and transformations from sequential patterns in the H-form and Hform into (H-)homomorphism are shown. We illustrate the power of our formalization by developing a novel and general parallel program for a class of interesting and challenging problems, known as maximum marking problems.
12036966
Literature mining and database annotation of protein phosphorylation using a rule-based system
MOTIVATION
A large volume of experimental data on protein phosphorylation is buried in the fast-growing PubMed literature. While of great value, such information is limited in databases owing to the laborious process of literature-based curation. Computational literature mining holds promise to facilitate database curation.


RESULTS
A rule-based system, RLIMS-P (Rule-based LIterature Mining System for Protein Phosphorylation), was used to extract protein phosphorylation information from MEDLINE abstracts. An annotation-tagged literature corpus developed at PIR was used to evaluate the system for finding phosphorylation papers and extracting phosphorylation objects (kinases, substrates and sites) from abstracts. RLIMS-P achieved a precision and recall of 91.4 and 96.4% for paper retrieval, and of 97.9 and 88.0% for extraction of substrates and sites. Coupling the high recall for paper retrieval and high precision for information extraction, RLIMS-P facilitates literature mining and database annotation of protein phosphorylation.
39609881
Diffusion: Calculating Efficient Parallel Programs