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The NP-hard graph bisection problem is to partition the nodes of an undirected graph into two equal-sized groups so as to minimize the number of edges that cross the partition. The more general graph l-partition problem is to partition the nodes of an undirected graph into l equal-sized groups so as to minimize the total number of edges that cross between(More)
We consider the problem of designing DNA codes, namely sets of equi-length words over the alphabet [A, C, G, T] that satisfy certain combinatorial constraints. This problem is motivated by the task of reliably storing and retrieving information in synthetic DNA strands for use in DNA computing or as molecular bar codes in chemical libraries. The primary(More)
DNA and RNA strands are employed in novel ways in the construction of nanostructures, as molecular tags in libraries of polymers and in therapeutics. New software tools for prediction and design of molecular structure will be needed in these applications. The RNAsoft suite of programs provides tools for predicting the secondary structure of a pair of DNA or(More)
We present HotKnots, a new heuristic algorithm for the prediction of RNA secondary structures including pseudoknots. Based on the simple idea of iteratively forming stable stems, our algorithm explores many alternative secondary structures, using a free energy minimization algorithm for pseudoknot free secondary structures to identify promising candidate(More)
The function of many RNAs depends crucially on their structure. Therefore, the design of RNA molecules with specific structural properties has many potential applications, e.g. in the context of investigating the function of biological RNAs, of creating new ribozymes, or of designing artificial RNA nanostructures. Here, we present a new algorithm for(More)
We study parallel algorithms for the minimum spanning tree problem, based on the sequential algorithm of Borůvka. The target architectures for our algorithm are asynchronous, distributed-memory machines. Analysis of our parallel algorithm, on a simple model that is reminiscent of the LogP model, shows that in principle a speedup proportional to the number(More)
We investigate the computability of problems in probabilistic planning and partially observable infinite-horizon Markov decision processes. The undecidability of the string-existence problem for probabilistic finite automata is adapted to show that the following problem of plan existence in probabilistic planning is undecidable: given a probabilistic(More)
We survey a number of algorithms for the simple stochastic game problem, which is to determine the winning probability of a type of stochastic process, where the transitions are partially controlled by two players. We show that four natural approaches to solving the problem are incorrect, and present two new algorithms for the problem. The rst reduces the(More)
BACKGROUND We investigate the empirical complexity of the RNA secondary structure design problem, that is, the scaling of the typical difficulty of the design task for various classes of RNA structures as the size of the target structure is increased. The purpose of this work is to understand better the factors that make RNA structures hard to design for(More)