BACKGROUND: Since membrane protein structures are challenging to crystallize, computational approaches are essential for elucidating the sequence-to-structure relationships. Structural modeling of membrane proteins requires a multidimensional approach, and one critical geometric parameter is the rotational angle of transmembrane helices. Rotational angles of transmembrane helices are characterized by their folded structures and could be inferred by the hydrophobic moment; however, the folding mechanism of membrane proteins is not yet fully understood. The rotational angle of a transmembrane helix is related to the exposed surface of a transmembrane helix, since lipid exposure gives the degree of accessibility of each residue in lipid environment. To the best of our knowledge, there have been few advances in investigating whether an environment descriptor of lipid exposure could infer a geometric parameter of rotational angle. RESULTS: Here, we present an analysis of the relationship between rotational angles and lipid exposure and a support-vector-machine method, called TMexpo, for predicting both structural features from sequences. First, we observed from the development set of 89 protein chains that the lipid exposure, i.e., the relative accessible surface area (rASA) of residues in the lipid environment, generated from high-resolution protein structures could infer the rotational angles with a mean absolute angular error (MAAE) of 46.32˚. More importantly, the predicted rASA from TMexpo achieved an MAAE of 51.05˚, which is better than 71.47˚ obtained by the best of the compared hydrophobicity scales. Lastly, TMexpo outperformed the compared methods in rASA prediction on the independent test set of 21 protein chains and achieved an overall Matthew's correlation coefficient, accuracy, sensitivity, specificity, and precision of 0.51, 75.26%, 81.30%, 69.15%, and 72.73%, respectively. TMexpo is publicly available at http://bio-cluster.iis.sinica.edu.tw/TMexpo. CONCLUSIONS: TMexpo can better predict rASA and rotational angles than the compared methods. When rotational angles can be accurately predicted, free modeling of transmembrane protein structures in turn may benefit from a reduced complexity in ensembles with a significantly less number of packing arrangements. Furthermore, sequence-based prediction of both rotational angle and lipid exposure can provide essential information when high-resolution structures are unavailable and contribute to experimental design to elucidate transmembrane protein functions.

BACKGROUND: Identification of subcellular localization in proteins is crucial to elucidate cellular processes and molecular functions in a cell. However, given a tremendous amount of sequence data generated in the post-genomic era, determining protein localization based on biological experiments can be expensive and time-consuming. Therefore, developing prediction systems to analyze uncharacterised proteins efficiently has played an important role in high-throughput protein analyses. In a eukaryotic cell, many essential biological processes take place in the nucleus. Nuclear proteins shuttle between nucleus and cytoplasm based on recognition of nuclear translocation signals, including nuclear localization signals (NLSs) and nuclear export signals (NESs). Currently, only a few approaches have been developed specifically to predict nuclear localization using sequence features, such as putative NLSs. However, it has been shown that prediction coverage based on the NLSs is very low. In addition, most existing approaches only attained prediction accuracy and Matthew's correlation coefficient (MCC) around 54%~70% and 0.250~0.380 on independent test set, respectively. Moreover, no predictor can generate sequence motifs to characterize features of potential NESs, in which biological properties are not well understood from existing experimental studies. RESULTS: In this study, first we propose PSLNuc (Protein Subcellular Localization prediction for Nucleus) for predicting nuclear localization in proteins. First, for feature representation, a protein is represented by gapped-dipeptides and the feature values are weighted by homology information from a smoothed position-specific scoring matrix. After that, we incorporate probabilistic latent semantic indexing (PLSI) for feature reduction. Finally, the reduced features are used as input for a support vector machine (SVM) classifier. In addition to PSLNuc, we further identify gapped-dipeptide signatures for putative NLSs and NESs to develop a prediction method, PSLNTS (Protein Subcellular Localization prediction using Nuclear Translocation Signals). We apply PLSI to generate gapped-dipeptide signatures from both nuclear and non-nuclear proteins, and propose candidate sequence motifs for putative NLSs and NESs. Then, we incorporate only the proposed gapped-dipeptide signatures in an SVM classifier to mimic biological properties of NLSs and NESs for predicting nuclear localization in PSLNTS. CONCLUSIONS: Experiment results demonstrate that the proposed method shows a significant improvement for nuclear localization prediction. To compare our predictive performance with other approaches, we incorporate two non-redundant benchmark data sets, a training set and an independent test set. Evaluated by five-fold cross-validation on the training set, PSLNuc attains an overall accuracy of 79.7%, which is 4.8% improvement over the state-of-the-art system. In addition, our method also enhances the MCC from 0.497 to 0.595. Compared on the independent test set, PSLNuc outperforms other predictors by 3.9%~19.9% on accuracy and 0.077~0.207 on MCC. This suggests that, in addition to NLSs, which have been shown important for nuclear proteins, NESs can also be an effective indicator to detect non-nuclear proteins. Most notably, using only a few proposed gapped-dipeptide signatures as input features for the SVM classifier, PSLNTS further enhances the accuracy and MCC to 80.9% and 0.618, respectively. Our results demonstrate that gapped-dipeptide signatures can better discriminate nuclear and non-nuclear proteins. Moreover, the proposed gapped-dipeptide signatures can be biologically interpreted and used in further experiment analyses of nuclear translocation signals, including NLSs and NESs.

MOTIVATION: Helix-helix interactions play a critical role in the structure assembly, stability and function of membrane proteins. On the molecular level, the interactions are mediated by one or more residue contacts. Although previous studies focused on helix-packing patterns and sequence motifs, few of them developed methods specifically for contact prediction. RESULTS: We present a new hierarchical framework for contact prediction, with an application in membrane proteins. The hierarchical scheme consists of two levels: in the first level, contact residues are predicted from the sequence and their pairing relationships are further predicted in the second level. Statistical analyses on contact propensities are combined with other sequence and structural information for training the support vector machine classifiers. Evaluated on 52 protein chains using leave-one-out cross validation (LOOCV) and an independent test set of 14 protein chains, the two-level approach consistently improves the conventional direct approach in prediction accuracy, with 80% reduction of input for prediction. Furthermore, the predicted contacts are then used to infer interactions between pairs of helices. When at least three predicted contacts are required for an inferred interaction, the accuracy, sensitivity and specificity are 56%, 40% and 89%, respectively. Our results demonstrate that a hierarchical framework can be applied to eliminate false positives (FP) while reducing computational complexity in predicting contacts. Together with the estimated contact propensities, this method can be used to gain insights into helix-packing in membrane proteins.

BACKGROUND: The study of protein subcellular localization (PSL) is important for elucidating protein functions involved in various cellular processes. However, determining the localization sites of a protein through wet-lab experiments can be time-consuming and labor-intensive. Thus, computational approaches become highly desirable. Most of the PSL prediction systems are established for single-localized proteins. However, a significant number of eukaryotic proteins are known to be localized into multiple subcellular organelles. Many studies have shown that proteins may simultaneously locate or move between different cellular compartments and be involved in different biological processes with different roles. RESULTS: In this study, we propose a knowledge based method, called KnowPredsite, to predict the localization site(s) of both single-localized and multi-localized proteins. Based on the local similarity, we can identify the "related sequences" for prediction. We construct a knowledge base to record the possible sequence variations for protein sequences. When predicting the localization annotation of a query protein, we search against the knowledge base and used a scoring mechanism to determine the predicted sites. We downloaded the dataset from ngLOC, which consisted of ten distinct subcellular organelles from 1923 species, and performed ten-fold cross validation experiments to evaluate KnowPred site's performance. The experiment results show that KnowPred site achieves higher prediction accuracy than ngLOC and Blast-hit method. For single-localized proteins, the overall accuracy of KnowPred site is 91.7%. For multi-localized proteins, the overall accuracy of KnowPred site is 72.1%, which is significantly higher than that of ngLOC by 12.4%. Notably, half of the proteins in the dataset that cannot find any Blast hit sequence above a specified threshold can still be correctly predicted by KnowPred site. CONCLUSION: KnowPred site demonstrates the power of identifying related sequences in the knowledge base. The experiment results show that even though the sequence similarity is low, the local similarity is effective for prediction. Experiment results show that KnowPred site is a highly accurate prediction method for both single- and multi-localized proteins. It is worth-mentioning the prediction process of KnowPred site is transparent and biologically interpretable and it shows a set of template sequences to generate the prediction result. The KnowPred site prediction server is available at http://bio-cluster.iis.sinica.edu.tw/kbloc/.

BACKGROUND: RNA-protein interaction plays an essential role in several biological processes, such as protein synthesis, gene expression, posttranscriptional regulation and viral infectivity. Identification of RNA-binding sites in proteins provides valuable insights for biologists. However, experimental determination of RNA-protein interaction remains time-consuming and labor-intensive. Thus, computational approaches for prediction of RNA-binding sites in proteins have become highly desirable. Extensive studies of RNA-binding site prediction have led to the development of several methods. However, they could yield low sensitivities in trade-off for high specificities. RESULTS: We propose a method, RNAProB, which incorporates a new smoothed position-specific scoring matrix (PSSM) encoding scheme with a support vector machine model to predict RNA-binding sites in proteins. Besides the incorporation of evolutionary information from standard PSSM profiles, the proposed smoothed PSSM encoding scheme also considers the correlation and dependency from the neighboring residues for each amino acid in a protein. Experimental results show that smoothed PSSM encoding significantly enhances the prediction performance, especially for sensitivity. Using five-fold cross-validation, our method performs better than the state-of-the-art systems by 4.90%-6.83%, 0.88%-5.33%, and 0.10-0.23 in terms of overall accuracy, specificity, and Matthew's correlation coefficient, respectively. Most notably, compared to other approaches, RNAProB significantly improves sensitivity by 7.0%-26.9% over the benchmark data sets. To prevent data over fitting, a three-way data split procedure is incorporated to estimate the prediction performance. Moreover, physicochemical properties and amino acid preferences of RNA-binding proteins are examined and analyzed. CONCLUSION: Our results demonstrate that smoothed PSSM encoding scheme significantly enhances the performance of RNA-binding site prediction in proteins. This also supports our assumption that smoothed PSSM encoding can better resolve the ambiguity of discriminating between interacting and non-interacting residues by modelling the dependency from surrounding residues. The proposed method can be used in other research areas, such as DNA-binding site prediction, protein-protein interaction, and prediction of posttranslational modification sites.

BACKGROUND: The significant advances in microarray and proteomics analyses have resulted in an exponential increase in potential new targets and have promised to shed light on the identification of disease markers and cellular pathways. We aim to collect and decipher the HCC-related genes at the systems level. RESULTS: Here, we build an integrative platform, the Encyclopedia of Hepatocellular Carcinoma genes Online, dubbed EHCO http://ehco.iis.sinica.edu.tw, to systematically collect, organize and compare the pileup of unsorted HCC-related studies by using natural language processing and softbots. Among the eight gene set collections, ranging across PubMed, SAGE, microarray, and proteomics data, there are 2,906 genes in total; however, more than 77% genes are only included once, suggesting that tremendous efforts need to be exerted to characterize the relationship between HCC and these genes. Of these HCC inventories, protein binding represents the largest proportion (~25%) from Gene Ontology analysis. In fact, many differentially expressed gene sets in EHCO could form interaction networks (e.g. HBV-associated HCC network) by using available human protein-protein interaction datasets. To further highlight the potential new targets in the inferred network from EHCO, we combine comparative genomics and interactomics approaches to analyze 120 evolutionary conserved and overexpressed genes in HCC. 47 out of 120 queries can form a highly interactive network with 18 queries serving as hubs. CONCLUSION: This architectural map may represent the first step toward the attempt to decipher the hepatocarcinogenesis at the systems level. Targeting hubs and/or disruption of the network formation might reveal novel strategy for HCC treatment.

BACKGROUND: Protein subcellular localization is crucial for genome annotation, protein function prediction, and drug discovery. Determination of subcellular localization using experimental approaches is time-consuming; thus, computational approaches become highly desirable. Extensive studies of localization prediction have led to the development of several methods including composition-based and homology-based methods. However, their performance might be significantly degraded if homologous sequences are not detected. Moreover, methods that integrate various features could suffer from the problem of low coverage in high-throughput proteomic analyses due to the lack of information to characterize unknown proteins. RESULTS: We propose a hybrid prediction method for Gram-negative bacteria that combines a one-versus-one support vector machines (SVM) model and a structural homology approach. The SVM model comprises a number of binary classifiers, in which biological features derived from Gram-negative bacteria translocation pathways are incorporated. In the structural homology approach, we employ secondary structure alignment for structural similarity comparison and assign the known localization of the top-ranked protein as the predicted localization of a query protein. The hybrid method achieves overall accuracy of 93.7% and 93.2% using ten-fold cross-validation on the benchmark data sets. In the assessment of the evaluation data sets, our method also attains accurate prediction accuracy of 84.0%, especially when testing on sequences with a low level of homology to the training data. A three-way data split procedure is also incorporated to prevent overestimation of the predictive performance. In addition, we show that the prediction accuracy should be approximately 85% for non-redundant data sets of sequence identity less than 30%. CONCLUSION: Our results demonstrate that biological features derived from Gram-negative bacteria translocation pathways yield a significant improvement. The biological features are interpretable and can be applied in advanced analyses and experimental designs. Moreover, the overall accuracy of combining the structural homology approach is further improved, which suggests that structural conservation could be a useful indicator for inferring localization in addition to sequence homology. The proposed method can be used in large-scale analyses of proteomes.

BACKGROUND: Bioinformatics tools for automatic processing of biomedical literature are invaluable for both the design and interpretation of large-scale experiments. Many information extraction (IE) systems that incorporate natural language processing (NLP) techniques have thus been developed for use in the biomedical field. A key IE task in this field is the extraction of biomedical relations, such as protein-protein and gene-disease interactions. However, most biomedical relation extraction systems usually ignore adverbial and prepositional phrases and words identifying location, manner, timing, and condition, which are essential for describing biomedical relations. Semantic role labeling (SRL) is a natural language processing technique that identifies the semantic roles of these words or phrases in sentences and expresses them as predicate-argument structures. We construct a biomedical SRL system called BIOSMILE that uses a maximum entropy (ME) machine-learning model to extract biomedical relations. BIOSMILE is trained on BioProp, our semi-automatic, annotated biomedical proposition bank. Currently, we are focusing on 30 biomedical verbs that are frequently used or considered important for describing molecular events. RESULTS: To evaluate the performance of BIOSMILE, we conducted two experiments to (1) compare the performance of SRL systems trained on newswire and biomedical corpora; and (2) examine the effects of using biomedical-specific features. The experimental results show that using BioProp improves the F-score of the SRL system by 21.45% over an SRL system that uses a newswire corpus. It is noteworthy that adding automatically generated template features improves the overall F-score by a further 0.52%. Specifically, ArgM-LOC, ArgM-MNR, and Arg2 achieve statistically significant performance improvements of 3.33%, 2.27%, and 1.44%, respectively. CONCLUSION: We demonstrate the necessity of using a biomedical proposition bank for training SRL systems in the biomedical domain. Besides the different characteristics of biomedical and newswire sentences, factors such as cross-domain framesets and verb usage variations also influence the performance of SRL systems. For argument classification, we find that NE (named entity) features indicating if the target node matches with NEs are not effective, since NEs may match with a node of the parsing tree that does not have semantic role labels in the training set. We therefore incorporate templates composed of specific words, NE types, and POS tags into the SRL system. As a result, the classification accuracy for adjunct arguments, which is especially important for biomedical SRL, is improved significantly.

BACKGROUND: Biomedical named entity recognition (Bio-NER) is a challenging problem because, in general, biomedical named entities of the same category (e.g., proteins and genes) do not follow one standard nomenclature. They have many irregularities and sometimes appear in ambiguous contexts. In recent years, machine-learning (ML) approaches have become increasingly common and now represent the cutting edge of Bio-NER technology. This paper addresses three problems faced by ML-based Bio-NER systems. First, most ML approaches usually employ singleton features that comprise one linguistic property (e.g., the current word is capitalized) and at least one class tag (e.g., B-protein, the beginning of a protein name). However, such features may be insufficient in cases where multiple properties must be considered. Adding conjunction features that contain multiple properties can be beneficial, but it would be infeasible to include all conjunction features in an NER model since memory resources are limited and some features are ineffective. To resolve the problem, we use a sequential forward search algorithm to select an effective set of features. Second, variations in the numerical parts of biomedical terms (e.g., "2" in the biomedical term IL2) cause data sparseness and generate many redundant features. In this case, we apply numerical normalization, which solves the problem by replacing all numerals in a term with one representative numeral to help classify named entities. Third, the assignment of NE tags does not depend solely on the target word's closest neighbors, but may depend on words outside the context window (e.g., a context window of five consists of the current word plus two preceding and two subsequent words). We use global patterns generated by the Smith-Waterman local alignment algorithm to identify such structures and modify the results of our ML-based tagger. This is called pattern-based post-processing. RESULTS: To develop our ML-based Bio-NER system, we employ conditional random fields, which have performed effectively in several well-known tasks, as our underlying ML model. Adding selected conjunction features, applying numerical normalization, and employing pattern-based post-processing improve the F-scores by 1.67%, 1.04%, and 0.57%, respectively. The combined increase of 3.28% yields a total score of 72.98%, which is better than the baseline system that only uses singleton features. CONCLUSION: We demonstrate the benefits of using the sequential forward search algorithm to select effective conjunction feature groups. In addition, we show that numerical normalization can effectively reduce the number of redundant and unseen features. Furthermore, the Smith-Waterman local alignment algorithm can help ML-based Bio-NER deal with difficult cases that need longer context windows.

BACKGROUND: Text mining in the biomedical domain is receiving increasing attention. A key component of this process is named entity recognition (NER). Generally speaking, two annotated corpora, GENIA and GENETAG, are most frequently used for training and testing biomedical named entity recognition (Bio-NER) systems. JNLPBA and BioCreAtIvE are two major Bio-NER tasks using these corpora. Both tasks take different approaches to corpus annotation and use different matching criteria to evaluate system performance. This paper details these differences and describes alternative criteria. We then examine the impact of different criteria and annotation schemes on system performance by retesting systems participated in the above two tasks. RESULTS: To analyze the difference between JNLPBA's and BioCreAtIvE's evaluation, we conduct Experiment 1 to evaluate the top four JNLPBA systems using BioCreAtIvE's classification scheme. We then compare them with the top four BioCreAtIvE systems. Among them, three systems participated in both tasks, and each has an F-score lower on JNLPBA than on BioCreAtIvE. In Experiment 2, we apply hypothesis testing and correlation coefficient to find alternatives to BioCreAtIvE's evaluation scheme. It shows that right-match and left-match criteria have no significant difference with BioCreAtIvE. In Experiment 3, we propose a customized relaxed-match criterion that uses right match and merges JNLPBA's five NE classes into two, which achieves an F-score of 81.5%. In Experiment 4, we evaluate a range of five matching criteria from loose to strict on the top JNLPBA system and examine the percentage of false negatives. Our experiment gives the relative change in precision, recall and F-score as matching criteria are relaxed. CONCLUSION: In many applications, biomedical NEs could have several acceptable tags, which might just differ in their left or right boundaries. However, most corpora annotate only one of them. In our experiment, we found that right match and left match can be appropriate alternatives to JNLPBA and BioCreAtIvE's matching criteria. In addition, our relaxed-match criterion demonstrates that users can define their own relaxed criteria that correspond more realistically to their application requirements.

MOTIVATION: In our previous approach, we proposed a hybrid method for protein secondary structure prediction called HYPROSP, which combined our proposed knowledge-based prediction algorithm PROSP and PSIPRED. The knowledge base constructed for PROSP contains small peptides together with their secondary structural information. The hybrid strategy of HYPROSP uses a global quantitative measure, match rate, to determine whether PROSP or PSIPRED is to be used for the prediction of a target protein. HYPROSP made slight improvement of Q(3) over PSIPRED because PROSP predicted well for proteins with match rate >80%. As the portion of proteins with match rate >80% is quite small and as the performance of PSIPRED also improves, the advantage of HYPROSP is diluted. To overcome this limitation and further improve the hybrid prediction method, we present in this paper a new hybrid strategy HYPROSP II that is based on a new quantitative measure called local match rate. RESULTS: Local match rate indicates the amount of structural information that each amino acid can extract from the knowledge base. With the local match rate, we are able to define a confidence level of the PROSP prediction results for each amino acid. Our new hybrid approach, HYPROSP II, is proposed as follows: for each amino acid in a target protein, we combine the prediction results of PROSP and PSIPRED using a hybrid function defined on their respective confidence levels. Two datasets in nrDSSP and EVA are used to perform a 10-fold cross validation. The average Q(3) of HYPROSP II is 81.8% and 80.7% on nrDSSP and EVA datasets, respectively, which is 2.0% and 1.1% better than that of PSIPRED. For local structures with match rate >80%, the average Q(3) improvement is 4.4% on the nrDSSP dataset. The use of local match rate improves the accuracy better than global match rate. There has been a long history of attempts to improve secondary structure prediction. We believe that HYPROSP II has greatly utilized the power of peptide knowledge base and raised the prediction accuracy to a new high. The method we developed in this paper could have a profound effect on the general use of knowledge base techniques for various predictionalgorithms. AVAILABILITY: The Linux executable file of HYPROSP II, as well as both nrDSSP and EVA datasets can be downloaded from http://bioinformatics.iis.sinica.edu.tw/HYPROSPII/.

NMR spectroscopy is one of the popular experiments to determine protein structures. An important stage of protein structure determination by using NMR is protein backbone resonance assignment (or backbone assignment for short). Due to the messiness and disorder of NMR spectral data, backbone assignment is usually a tedious and time-consuming manual work. This raises a great interest in developing an efficient and automatic method to perform backbone assignment. An iterative algorithm is proposed that is equipped with two operations: grouping and linking. Grouping is responsible for peak picking and part of connectivity determination. Ideally, those peaks with the same H/sup N/ and N chemical shifts can be grouped together; peaks belonging to the same group can be used to determine the order of two consecutive spin systems. However, in real situation, grouping is a difficult task due to false positives and false negatives. We sometimes add hypothetic peaks to tackle false negatives and use linking operation to remove false positives. Linking is responsible for part of connectivity determination and backbone assignment. Given a protein sequence and partial connectivity information, we try to link connected spin systems as much as possible. False positive spin systems may create conflicts in the linking stage. To find a good assignment on a noisy dataset, the backbone assignment problem is modeled as a maximum independent set problem. Although the problem is NP-complete, there are heuristic methods that obtain pretty good results.

Abstract A graphGis a combinedk‐fault‐tolerant Hamiltonian graph (also called a combinedk‐Hamiltonian graph) ifG−Fis Hamiltonian for every subsetF⊂ (V(G) ∪E(G)) with |F| =k. A combinedk‐Hamiltonian graphGwith |V(G)| =nis optimal if it has the minimum number of edges among alln‐nodek‐Hamiltonian graphs. Using the concept of node expansion, we present a powerful construction scheme to construct a larger combinedk‐Hamiltonian graph from a given smaller graph. Many previous graphs can be constructed by the concept of node expansion. We also show that our construction maintains the optimality property in most cases. The classes of optimal combinedk‐Hamiltonian graphs that we constructed are shown to have a very good diameter. In particular, those optimal combined 1‐Hamiltonian graphs that we constructed have a much smaller diameter than that of those constructed previously by Mukhopadhyaya and Sinha, Harary and Hayes, and Wang et al. © 2001 John Wiley & Sons, Inc.

In this paper, we present three construction schemes for fault-tolerant Hamiltonian graphs. We show that applying these construction schemes on fault-tolerant Hamiltonian graphs generates graphs preserving the original Hamiltonicity property. We apply these construction schemes to generate some known families of optimal 1-Hamiltonian graphs in the literature and the Hamiltonicity properties of these graphs are the direct consequence of the construction schemes. In addition, we can use these construction schemes to propose new family of optimal 1-Hamiltonian graphs. © 2000 John Wiley & Sons, Inc.

An n-dimensional crossed cube, CQ/sub n/, is a variation of hypercubes. In this paper, we give a new shortest path routing algorithm based on a new distance measure defined herein. In comparison with Efe's algorithm, which generates one shortest path in O(n/sup 2/) time, our algorithm can generate more shortest paths in O(n) time. Based on a given shortest path routing algorithm, we consider a new performance measure of interconnection networks called edge congestion. Using our shortest path routing algorithm and assuming that message exchange between all pairs of vertices is equally probable, we show that the edge congestion of crossed cubes is the same as that of hypercubes. Using the result of edge congestion, we can show that the bisection width of crossed cubes is 2/sup n-1/. We also prove that wide diameter and fault diameter are [n/2]+2. Furthermore, we study embedding of cycles in cross cubes and construct more types than previous work of cycles of length at least four.

We show that the cyclic-cubes defined by Ada W.C. Fu and S.C. Chau (1998) are isomorphic to k-ary wrapped butterfly networks.

The token ring topology is required in the token passing approach used in distributed operating systems. Fault tolerance is also required in the design of distributed systems. We consider the 1-fault-tolerant design for token rings, which can tolerate 1-processor fault- or 1-link fault. Note that the 1-fault-tolerant design for token rings is equivalent to the design of 1-Hamiltonian graphs. The paper introduces a new family of interconnection networks called Christmas tree. The under graph of the Christmas tree, denoted by CT(s), is a 3-regular, planar, 1-Hamiltonian, and Hamiltonian-connected graph. The number of nodes and the diameter of CT(s) are 3/spl times/2/sup s/-2 and 2s, respectively. In other words, the diameter of CT(s) is 2 log/sub 2/ n-O(1), where n is the number of nodes.

Previous works on edge-fault tolerance with respect to hypercubes Q/sub n/ are mainly focused on 1-edge fault and 2- or 3-edge fault with limited size of n. We give a construction scheme for 2-EFT(Q/sub n/) graphs and 3-EFT(Q/sub n/) graphs, where n is arbitrarily large. In our constructions, approximately log n extra degree is added to the vertices of Q/sub n/ for 2-edge-fault tolerance, and one more degree for 3-edge-fault tolerance.

Architectures for interconnection networks can be represented by graphs, while vertices represent processors and edges represent communication links between processors. We use the terms vertices and processors interchangeably. Let G = (V, E) be a graph representing the topology for an interconnection network. Let v0 be a special vertex outside G, called the host processor, which is connected to each vertex in G. The host processor is the sender or source of the message to be transmitted to all of the vertices in G. In each time unit, the host processor may send an identical message to an arbitrary vertex in G or remain idle. At the same time, each processor in G that has already received the message can send it to all its neighbors in one time unit. A transmitting scheme allowing all processors to receive the message in t time units and requiring the host processor to send the message s times is called a (t, s)-transmitting scheme, where t ≥ s. We call t the transmitting time, and s, the workload of the host processor. We aimed to find an optimal transmitting scheme, i.e., a transmitting scheme such that t is minimized while s is also minimized. In this paper, we present optimal transmitting schemes for linear arrays, rings, complete binary trees, star trees, and (directed) de Bruijn graphs. Furthermore, we present a (t, s)-transmitting scheme for diagonal meshes which are defined slightly different from meshes, and the ratio of t to the optimal transmitting time is approximate to 1.1. © 1996 John Wiley & Sons, Inc.

De Bruijn graphs, both directed and undirected, have received considerable attention as architecture for interconnection networks. In this paper, we focus on undirected de Bruijn networks of radix d and dimension 0, denoted by UB(d, 0). We first discuss the shortest-path routing problem. We present properties of the shortest paths between any two vertices of UB(d, 0) and propose two shortest-path routing algorithms, one of which has linear time complexity. Secondly, we study the transmitting problem. We establish a lower bound for the optimal transmitting time which implies in particular that the optimal transmitting problem is trivial for UB(d, 0) when d/spl ges/5. We present a transmitting scheme on undirected binary de Bruijn networks UB(2, n) with transmitting time n-1 for n/spl ges/5, and conjecture that the optimal transmitting time is n-1 for UB(2, n), and n for U8(3, n) and UB(4, n).

Abstract Let G = (V,E) be an undirected graph having an edge weight we ≥ 0 for each e ϵ E. An edge is called a most vital edge (with respect to weighted matching) if its removal from G results in the largest decrease in the total weight of the maximum weighted matching. In this paper, we study the most vital edges of matching in a weighted bipartite graph. We present an O(n3) algorithm to obtain the most vital edges. © 1993 by John Wiley & Sons, Inc.