MOTIVATION: Knowledge of the 3D structure of RNA supports discovering its functions and is crucial for designing drugs and modern therapeutic solutions. Thus, much attention is devoted to experimental determination and computational prediction targeting the global fold of RNA and its local substructures. The latter include multi-branched loops-functionally significant elements that highly affect the spatial shape of the entire molecule. Unfortunately, their computational modeling constitutes a weak point of structural bioinformatics. A remedy for this is in collecting these motifs and analyzing their features. RESULTS: RNAloops is a self-updating database that stores multi-branched loops identified in the PDB-deposited RNA structures. A description of each loop includes angular data-planar and Euler angles computed between pairs of adjacent helices to allow studying their mutual arrangement in space. The system enables search and analysis of multiloops, presents their structure details numerically and visually, and computes data statistics. AVAILABILITY AND IMPLEMENTATION: RNAloops is freely accessible at https://rnaloops.cs.put.poznan.pl. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We present an approach to discriminate SARS-CoV-2 virus types based on their RNA sequence descriptions avoiding a sequence alignment. For that purpose, sequences are preprocessed by feature extraction and the resulting feature vectors are analyzed by prototype-based classification to remain interpretable. In particular, we propose to use variants of learning vector quantization (LVQ) based on dissimilarity measures for RNA sequence data. The respective matrix LVQ provides additional knowledge about the classification decisions like discriminant feature correlations and, additionally, can be equipped with easy to realize reject options for uncertain data. Those options provide self-controlled evidence, i.e., the model refuses to make a classification decision if the model evidence for the presented data is not sufficient. This model is first trained using a GISAID dataset with given virus types detected according to the molecular differences in coronavirus populations by phylogenetic tree clustering. In a second step, we apply the trained model to another but unlabeled SARS-CoV-2 virus dataset. For these data, we can either assign a virus type to the sequences or reject atypical samples. Those rejected sequences allow to speculate about new virus types with respect to nucleotide base mutations in the viral sequences. Moreover, this rejection analysis improves model robustness. Last but not least, the presented approach has lower computational complexity compared to methods based on (multiple) sequence alignment. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00521-021-06018-2.

MOTIVATION: Viruses are the most abundant biological entities and constitute a large reservoir of genetic diversity. In recent years, knowledge about them has increased significantly as a result of dynamic development in life sciences and rapid technological progress. This knowledge is scattered across various data repositories, making a comprehensive analysis of viral data difficult. RESULTS: In response to the need for gathering a comprehensive knowledge of viruses and viral sequences, we developed Virxicon, a lexicon of all experimentally acquired sequences for RNA and DNA viruses. The ability to quickly obtain data for entire viral groups, searching sequences by levels of taxonomic hierarchy-according to the Baltimore classification and ICTV taxonomy-and tracking the distribution of viral data and its growth over time are unique features of our database compared to the other tools. AVAILABILITYAND IMPLEMENTATION: Virxicon is a publicly available resource, updated weekly. It has an intuitive web interface and can be freely accessed at http://virxicon.cs.put.poznan.pl/.

MOTIVATION: There are very few methods for de novo genome assembly based on the overlap graph approach. It is considered as giving more exact results than the so-called de Bruijn graph approach but in much greater time and of much higher memory usage. It is not uncommon that assembly methods involving the overlap graph model are not able to successfully compute greater datasets, mainly due to memory limitation of a computer. This was the reason for developing in last decades mainly de Bruijn-based assembly methods, fast and fairly accurate. However, the latter methods can fail for longer or more repetitive genomes, as they decompose reads to shorter fragments and lose a part of information. An efficient assembler for processing big datasets and using the overlap graph model is still looked out. RESULTS: We propose a new genome-scale de novo assembler based on the overlap graph approach, designed for short-read sequencing data. The method, ALGA, incorporates several new ideas resulting in more exact contigs produced in short time. Among these ideas, we have creation of a sparse but quite informative graph, reduction of the graph including a procedure referring to the problem of minimum spanning tree of a local subgraph, and graph traversal connected with simultaneous analysis of contigs stored so far. What is rare in genome assembly, the algorithm is almost parameter-free, with only one optional parameter to be set by a user. ALGA was compared with nine state-of-the-art assemblers in tests on genome-scale sequencing data obtained from real experiments on six organisms, differing in size, coverage, GC content and repetition rate. ALGA produced best results in the sense of overall quality of genome reconstruction, understood as a good balance between genome coverage, accuracy and length of resulting sequences. The algorithm is one of tools involved in processing data in currently realized national project Genomic Map of Poland. AVAILABILITY AND IMPLEMENTATION: ALGA is available at http://alga.put.poznan.pl. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Motivation: In the study of 3D RNA structure, information about non-canonical interactions between nucleobases is increasingly important. Specialized databases support investigation of this issue based on experimental data, and several programs can annotate non-canonical base pairs in the RNA 3D structure. However, predicting the extended RNA secondary structure which describes both canonical and non-canonical interactions remains difficult. Results: Here, we present RNAvista that allows predicting an extended RNA secondary structure from sequence or from the list enumerating canonical base pairs only. RNAvista is implemented as a publicly available webserver with user-friendly interface. It runs on all major web browsers. Availability and implementation: http://rnavista.cs.put.poznan.pl.

BACKGROUND: Structural alignment of proteins is one of the most challenging problems in molecular biology. The tertiary structure of a protein strictly correlates with its function and computationally predicted structures are nowadays a main premise for understanding the latter. However, computationally derived 3D models often exhibit deviations from the native structure. A way to confirm a model is a comparison with other structures. The structural alignment of a pair of proteins can be defined with the use of a concept of protein descriptors. The protein descriptors are local substructures of protein molecules, which allow us to divide the original problem into a set of subproblems and, consequently, to propose a more efficient algorithmic solution. In the literature, one can find many applications of the descriptors concept that prove its usefulness for insight into protein 3D structures, but the proposed approaches are presented rather from the biological perspective than from the computational or algorithmic point of view. Efficient algorithms for identification and structural comparison of descriptors can become crucial components of methods for structural quality assessment as well as tertiary structure prediction. RESULTS: In this paper, we propose a new combinatorial model and new polynomial-time algorithms for the structural alignment of descriptors. The model is based on the maximum-size assignment problem, which we define here and prove that it can be solved in polynomial time. We demonstrate suitability of this approach by comparison with an exact backtracking algorithm. Besides a simplification coming from the combinatorial modeling, both on the conceptual and complexity level, we gain with this approach high quality of obtained results, in terms of 3D alignment accuracy and processing efficiency. CONCLUSIONS: All the proposed algorithms were developed and integrated in a computationally efficient tool descs-standalone, which allows the user to identify and structurally compare descriptors of biological molecules, such as proteins and RNAs. Both PDB (Protein Data Bank) and mmCIF (macromolecular Crystallographic Information File) formats are supported. The proposed tool is available as an open source project stored on GitHub ( https://github.com/mantczak/descs-standalone ).

DOAJ is a unique and extensive index of diverse open access journals from around the world, driven by a growing community, committed to ensuring quality content is freely available online for everyone.

3D protein structure prediction is of significant interest in the biological research community. Nowadays, one can find many methodologies that can lead to model protein structures, and for that reason the plausible assessment of the quality of protein structural models has fundamental impact on the progress of structural bioinformatics. Here, we present SphereGrinder, a novel computational tool devoted to evaluation of protein 3D models according to the reference structure that gives an opportunity to proceed with structural analysis from atomic to the whole molecule level of accuracy. Proposed tool is capable of handling large predicted models set is designed and used for protein structure prediction in CASP (Critical Assessment of Techniques for Protein Structure Prediction) experiment to complement and add value to the traditional protein structure quality assessment by the global distance test and related scores. SphereGrinder is a user-friendly software that allows the comprehensive quality inspection conducted between the set of predicted protein models and the reference structure. It is implemented as an online application available for free use by all academic users at the URL http://spheregrinder.cs.put.poznan.pl.

BACKGROUND: The function of RNA is strongly dependent on its structure, so an appropriate recognition of this structure, on every level of organization, is of great importance. One particular concern is the assessment of base-base interactions, described as the secondary structure, the knowledge of which greatly facilitates an interpretation of RNA function and allows for structure analysis on the tertiary level. The RNA secondary structure can be predicted from a sequence using in silico methods often adjusted with experimental data, or assessed from 3D structure atom coordinates. Computational approaches typically consider only canonical, Watson-Crick and wobble base pairs. Handling of non-canonical interactions, important for a full description of RNA structure, is still very difficult. RESULTS: We introduce our novel approach to assessing an extended RNA secondary structure, which characterizes both canonical and non-canonical base pairs, along with their type classification. It is based on predicting the RNA 3D structure from a user-provided sequence or a secondary structure that only describes canonical base pairs, and then deriving the extended secondary structure from atom coordinates. In our example implementation, this was achieved by integrating the functionality of two fully automated, high fidelity methods in a computational pipeline: RNAComposer for the 3D RNA structure prediction and RNApdbee for base-pair annotation. CONCLUSIONS: The presented methodology ties together existing applications for RNA 3D structure prediction and base-pair annotation. The example performance, applying RNAComposer and RNApdbee, reveals better accuracy in non-canonical base pair assessment than the compared methods that directly predict RNA secondary structure.

BACKGROUND: The lack of a uniform way for qualitative and quantitative evaluation of vaccine candidates under development led us to set up a standardized scheme for vaccine efficacy and safety evaluation. We developed and implemented molecular and immunology methods, and designed support tools for immunization data storage and analyses. Such collection can create a unique opportunity for immunologists to analyse data delivered from their laboratories. RESULTS: We designed and implemented GeVaDSs (Genetic Vaccine Decision Support system) an interactive system for efficient storage, integration, retrieval and representation of data. Moreover, GeVaDSs allows for relevant association and interpretation of data, and thus for knowledge-based generation of testable hypotheses of vaccine responses. CONCLUSIONS: GeVaDSs has been tested by several laboratories in Europe, and proved its usefulness in vaccine analysis. Case study of its application is presented in the additional files. The system is available at: http://gevads.cs.put.poznan.pl/preview/(login: viewer, password: password).

The results presented in the paper are threefold. Firstly, a new class of reduced-by-matching directed graphs is defined and its properties studied. The graphs are output from the algorithm which, for a given 1-graph, removes arcs which are unnecessary from the point of view of searching for a Hamiltonian circuit. In the best case, the graph is reduced to a quasi-adjoint graph, what results in polynomial-time solution of the Hamiltonian circuit problem. Secondly, the systematization of several classes of digraphs, known from the literature and referring to directed line graphs, is provided together with the proof of its correctness. Finally, computational experiments are presented in order to verify the effectiveness of the reduction algorithm.

The progress of research in the area of computational biology, visible in last decades, brought, among others, a new insight into the complexity issues. The latter, previously studied mainly on the ground of computer science or operational research,

BACKGROUND: Pairwise sequence alignment methods are widely used in biological research. The increasing number of sequences is perceived as one of the upcoming challenges for sequence alignment methods in the nearest future. To overcome this challenge several GPU (Graphics Processing Unit) computing approaches have been proposed lately. These solutions show a great potential of a GPU platform but in most cases address the problem of sequence database scanning and computing only the alignment score whereas the alignment itself is omitted. Thus, the need arose to implement the global and semiglobal Needleman-Wunsch, and Smith-Waterman algorithms with a backtracking procedure which is needed to construct the alignment. RESULTS: In this paper we present the solution that performs the alignment of every given sequence pair, which is a required step for progressive multiple sequence alignment methods, as well as for DNA recognition at the DNA assembly stage. Performed tests show that the implementation, with performance up to 6.3 GCUPS on a single GPU for affine gap penalties, is very efficient in comparison to other CPU and GPU-based solutions. Moreover, multiple GPUs support with load balancing makes the application very scalable. CONCLUSIONS: The article shows that the backtracking procedure of the sequence alignment algorithms may be designed to fit in with the GPU architecture. Therefore, our algorithm, apart from scores, is able to compute pairwise alignments. This opens a wide range of new possibilities, allowing other methods from the area of molecular biology to take advantage of the new computational architecture. Performed tests show that the efficiency of the implementation is excellent. Moreover, the speed of our GPU-based algorithms can be almost linearly increased when using more than one graphics card.

This paper presents a parallel branch-and-bound method to address the two-dimensional rectangular guillotine strip cutting problem. Our paper focuses on a parallel branching schema. We present a series of computational experiments to evaluate the strength of the approach. Optimal solutions have been found for some benchmark instances that had unknown solutions until now. For many other instances, we demonstrate that the proposed approach is time effective. The efficiency of the parallel version of the algorithm is compared and the speedup, when increasing the number of processors, is clearly demonstrated with an upper bound calculated by a specialised heuristic procedure.

BACKGROUND: Recent discoveries concerning novel functions of RNA, such as RNA interference, have contributed towards the growing importance of the field. In this respect, a deeper knowledge of complex three-dimensional RNA structures is essential to understand their new biological functions. A number of bioinformatic tools have been proposed to explore two major structural databases (PDB, NDB) in order to analyze various aspects of RNA tertiary structures. One of these tools is RNA FRABASE 1.0, the first web-accessible database with an engine for automatic search of 3D fragments within PDB-derived RNA structures. This search is based upon the user-defined RNA secondary structure pattern. In this paper, we present and discuss RNA FRABASE 2.0. This second version of the system represents a major extension of this tool in terms of providing new data and a wide spectrum of novel functionalities. An intuitionally operated web server platform enables very fast user-tailored search of three-dimensional RNA fragments, their multi-parameter conformational analysis and visualization. DESCRIPTION: RNA FRABASE 2.0 has stored information on 1565 PDB-deposited RNA structures, including all NMR models. The RNA FRABASE 2.0 search engine algorithms operate on the database of the RNA sequences and the new library of RNA secondary structures, coded in the dot-bracket format extended to hold multi-stranded structures and to cover residues whose coordinates are missing in the PDB files. The library of RNA secondary structures (and their graphics) is made available. A high level of efficiency of the 3D search has been achieved by introducing novel tools to formulate advanced searching patterns and to screen highly populated tertiary structure elements. RNA FRABASE 2.0 also stores data and conformational parameters in order to provide "on the spot" structural filters to explore the three-dimensional RNA structures. An instant visualization of the 3D RNA structures is provided. RNA FRABASE 2.0 is freely available at http://rnafrabase.cs.put.poznan.pl. CONCLUSIONS: RNA FRABASE 2.0 provides a novel database and powerful search engine which is equipped with new data and functionalities that are unavailable elsewhere. Our intention is that this advanced version of the RNA FRABASE will be of interest to all researchers working in the RNA field.

Nuclear Magnetic Resonance spectroscopy is an important technique to study structures of biomolecules. While it is possible to use two-dimensional experiments to determine RNA structures, multi-dimensional experiments ensure a better distribution of signals providing a clearer view of the intra- as well as inter-molecular correlations. In this paper, we propose a new graph model to represent three-dimensional homo- and heteronuclear NMR spectra. Following this, we present an enumerative algorithm for signal assignment in the spectra recorded for RNA molecules and we show its performance on exemplary data.

BACKGROUND: We introduce the decision support system for Protein (Structure) Comparison, Knowledge, Similarity and Information (ProCKSI). ProCKSI integrates various protein similarity measures through an easy to use interface that allows the comparison of multiple proteins simultaneously. It employs the Universal Similarity Metric (USM), the Maximum Contact Map Overlap (MaxCMO) of protein structures and other external methods such as the DaliLite and the TM-align methods, the Combinatorial Extension (CE) of the optimal path, and the FAST Align and Search Tool (FAST). Additionally, ProCKSI allows the user to upload a user-defined similarity matrix supplementing the methods mentioned, and computes a similarity consensus in order to provide a rich, integrated, multicriteria view of large datasets of protein structures. RESULTS: We present ProCKSI's architecture and workflow describing its intuitive user interface, and show its potential on three distinct test-cases. In the first case, ProCKSI is used to evaluate the results of a previous CASP competition, assessing the similarity of proposed models for given targets where the structures could have a large deviation from one another. To perform this type of comparison reliably, we introduce a new consensus method. The second study deals with the verification of a classification scheme for protein kinases, originally derived by sequence comparison by Hanks and Hunter, but here we use a consensus similarity measure based on structures. In the third experiment using the Rost and Sander dataset (RS126), we investigate how a combination of different sets of similarity measures influences the quality and performance of ProCKSI's new consensus measure. ProCKSI performs well with all three datasets, showing its potential for complex, simultaneous multi-method assessment of structural similarity in large protein datasets. Furthermore, combining different similarity measures is usually more robust than relying on one single, unique measure. CONCLUSION: Based on a diverse set of similarity measures, ProCKSI computes a consensus similarity profile for the entire protein set. All results can be clustered, visualised, analysed and easily compared with each other through a simple and intuitive interface.ProCKSI is publicly available at http://www.procksi.net for academic and non-commercial use.

We study the Simplified Partial Digest Problem (SPDP), which is a mathematical model for a new simplified partial digest method of genome mapping. This method is easy for laboratory implementation and robust with respect to the experimental errors. SPDP is NP-hard in the strong sense. We present an $O(n2;n)$ time enumerative algorithm and an O(n(2q)) time dynamic programming algorithm for the error-free SPDP, where $n$ is the number of restriction sites and n is the number of distinct intersite distances. We also give examples of the problem, in which there are 2(n+2)/(3)-1 non-congruent solutions. These examples partially answer a question recently posed in the literature about the number of solutions of SPDP. We adapt our enumerative algorithm for handling SPDP with imprecise input data. Finally, we describe and discuss the results of the computer experiments with our algorithms.

The prediction of the coordination number (CN) of an amino acid in a protein structure has recently received renewed attention. In a recent paper, Kinjo et al. proposed a real-valued definition of CN and a criterion to map it onto a finite set of classes, in order to predict it using classification approaches. The literature reports several kinds of input information used for CN prediction. The aim of this paper is to assess the performance of a state-of-the-art learning method, Learning Classifier Systems (LCS) on this CN definition, with various degrees of precision, based on several combinations of input attributes. Moreover, we will compare the LCS performance to other well-known learning techniques. Our experiments are also intended to determinethe minimum set of input information needed to achieve good predictive performance, so as to generate competent yet simple and interpretable classification rules. Thus, the generated predictors (rule sets) are analyzed for their interpretability.

The problem of optimal scheduling n independent malleable tasks in a parallel processor system is studied. It is assumed that an execution of any task can be preempted and the number of processors allocated to the same task can change during its execution. We present a rectangle packing algorithm, which converts an optimal solution for the relaxed problem, in which the number of processors allocated to a task is not required to be integer, into an optimal solution for the original problem in O(n) time.

MOTIVATION: Liquid state nuclear magnetic resonance (NMR) spectroscopy has now been well established as a method for RNA tertiary structure determination. Most of the steps involved in the determination of RNA molecules are performed using computer programs. They however, do not apply to resonance assignment being the starting point of the whole procedure. We propose a tabu search algorithm as a tool for automating this step. Nuclear overhause effect (NOE) pathway, which determines the assignment, is constructed during an analysis of possible connections between resonances within aromatic/anomeric region of two-dimensional NOESY spectrum resulting from appropriate NMR experiment. RESULTS: Computational tests demonstrate the superior performance of the tabu search algorithm as compared with the exact enumerative approach and genetic procedure applied to the experimental and simulated spectral data for RNA molecules. AVAILABILITY: The software package can be obtained upon request from Marta Szachniuk.

Resonance assignment remains one of the hardest stages in RNA tertiary structure elucidation with the use of nuclear magnetic resonance spectroscopy. We propose an evolutionary algorithm being a tool for an automatic design of the procedure. NOE pathway, which determines the assignments, is constructed during an analysis of possible connections between resonances within aromatic/anomeric region of 2D-NOESY spectra. Computational tests demonstrate the performance of the genetic algorithm in comparison with the enumerative procedure applied for the experimental and simulated spectral data for RNA molecules.

In this paper, a tabu-search algorithm enhanced by scatter search is presented. The algorithm solves the DNA sequencing problem with negative and positive errors, yielding outcomes of high quality. We compare the new method with two other metaheuristic approaches: a previous tabu-search method and a hybrid genetic algorithm, and also with an old branch-and-bound approach.

Abstract Motivation: A new heuristic algorithm for solving DNA sequencing by hybridization problem with positive and negative errors. Results: A heuristic algorithm providing better solutions than algorithms known from the literature based on tabu search method. Contact: [email protected] * To whom correspondence should be addressed.

Abstract Motivation: A formulation of a new problem of the restriction map construction based on a simplified digestion experiment and a development of an algorithm for solving both ideal and noisy data cases of the introduced problem. Results: A simplified partial digest problem and a branch and cut algorithm for finding the solution of the problem. Contact: [email protected] * To whom correspondence should be addressed. † Fellowship holder of the Foundation for Polish Sciences.

MOTIVATION: Reconstruction of the original DNA sequence in the sequencing by the hybridization approach (SBH) requires computational support due to a large number of possible combinations. One can notice a lack of algorithms admitting false-negative data and giving in addition all possible solutions. RESULTS: In this paper, a new method of sequencing has been proposed. An algorithm based on its idea (for the general case, when some data are missing, like in the real experiment) has been implemented and tested. Authentic DNA sequences have been used for testing. A parallel version of the algorithm has also been implemented and tested. The quality of the reconstruction is satisfactory for the library of oligonucleotides of length between 8 and 12, and 100, 200 and 300 bp long sequences. A way to a further decrease in the computation time is also suggested.

A problem of deadlock avoidance in store-and-forward networks with at least two buffers per node is considered for fixed as well as dynamic routing. For both cases polynomial time, centralized deadlock avoidance algorithms are proposed and shown to be optimal in a sense of possible buffer utilization. When the number of buffers is equal to one for each node the problem is known to be NP-complete, thus, unlikely to admit a polynomial-time algorithm. The presented results may be also interesting for other applications, some massively parallel computer systems being one of the examples.>

An FMS is considered in which the AGV are operated in cyclic mode. This yields an efficient utilization of the AGVs with respect to the throughput rate for the material to be delivered. The FMS produces helicopter party. The aim is to solve simultaneously the machine and the vehicle scheduling problems. A dynamic programming approach can solve this problem in pseudo-polynomial time. In the case of a given production schedule, a polynomial-time algorithm is proposed that constructs a feasible vehicle schedule whenever one exists.>

This paper deals with the problem of store-and-forward deadlock prevention in store-and-forward networks. The presented solution uses time stamping of all messages in the network, and a nonpreemptable message exchange mechanism. By combining these ideas, a new distributed flow control procedure is derived which guarantees that all messages are delivered to their own destinations, thus avoiding both deadlock and livelock without any message loss. It is shown that some properties of this procedure depend on the policy of the allocation of exchange buffers to nodes. On the one hand, an optimal allocation strategy is presented which results in a maximally optimal deadlock prevention procedure. The procedure is network sizeand topology-independent and allows unrestricted packet routing. On the other hand, the allocation of one exchange buffer per node is discussed, which, even if not optimal, makes the derived deadlock prevention procedure completely independent of network reconfigurations. The last feature is extremely important from the practical point of view and, therefore, such a solution is strongly recommended. When compared to store-and-forward deadlock prevention procedures described so far, which lack some or all of these desirable properties, the procedure presented here behaves favorably. However, it imposes other drawbacks, i.e., the possibility of extra hops as a result of exchange operations. It is argued that this drawback appears rarely in practice, and some strategies which aim at a reduction of it are proposed.

This correspondence is concerned with the prevention of four types of deadlock in store-and-forward networks, i.e., progeny, copy-release, reassembly, and resequence deadlocks. The approach presented makes use of time stamping of all messages and generalizes the method of store-and-forward deadlock prevention.

The problem considered in this paper is the deterministic scheduling of tasks on a set of identical processors. However, the model presented differs from the classical one by the requirement that certain tasks need more than one processor at a time for their processing. This assumption is especially justified in some microprocessor applications and its impact on the complexity of minimizing schedule length is studied. First we concentrate on the problem of nonpreemptive scheduling. In this case, polynomial-time algorithms exist only for unit processing times. We present two such algorithms of complexity O(n) for scheduling tasks requiring an arbitrary number of processors between 1 and k at a time where k is a fixed integer. The case for which k is not fixed is shown to be NP-complete. Next, the problem of preemptive scheduling of tasks of arbitrary length is studied. First an algorithm for scheduling tasks requiring one or k processors is presented. Its complexity depends linearly on the number of tasks. Then, the possibility of a linear programming formulation for the general case is analyzed.

A flow control procedure for an acyclic store-and-forward network is introduced which uses only information local to each node and is deadlock-resistant (i.e., detects and recovers deadlock at a negligible cost). The procedure requires less than3n/2buffers (the exact value depending on the network topology), wherenis the number of nodes in the network. It is shown that this number is lower bound for distributed deadlock-resistant procedures. From a practical point of view, this means that a single buffer class is sufficient, provided that the exchange mechanism for input buffers is realized as a synchronized procedure between any two contiguous nodes (rather than as a purely local procedure). Some extension to more general networks are then proposed.

PurposeSubroutine A R S M E solves a resource constrained, network scheduling problem for the case in which activities may be arbitrarily interrupted and restarted later with no increase in activity duration.The number of resource types is not a limiting factor in our procedure.The amount of any one resource available at any moment is constant.We shall use the "activity-on-arc" network representation, under the commonly imposed assumption that the network contains no directed cycles and has only one "beginning" and only one "terminal" node (event).I t is further assumed that the network nodes (events) are ordered in such a way t h a t node i precedes node j, if i < j.Such an ordering is always possible and it induces an ordering among the arcs (activities).Optimal approaches to resource constrained, network scheduling problems where activities can require more than one resource type are presented in [1,4].Both methods assume integer durations of activities, and the method presented in [1] divides activity durations into unit intervals.Both methods can handle networks with up to about 30 activities and 3 resource types.Subroutine A R S M E is constructed in such a way that its storage requirements are minimal, a fact which permits the solution of problems for very large networks with many resource types.Moreover, an optimal solution can be obtained in a shorter time when relatively smaller amounts of the resources are available than when resources are less limited.Let the number of activities be equal to M and the number of resource types be equal to RT.For activityj (j = 1, 2 , . . ., M) and resource k (k = 1, 2 , . . ., RT)