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Minimum Common String Partition Parameterized
, 2007
"... Minimum Common String Partition (MCSP) and related problems are of interest in, e.g., comparative genomics, DNA fingerprint assembly, and ortholog assignment. Given two strings with equal symbol content, the problem is to partition one string into k blocks, k as small as possible, and to permute t ..."
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Minimum Common String Partition (MCSP) and related problems are of interest in, e.g., comparative genomics, DNA fingerprint assembly, and ortholog assignment. Given two strings with equal symbol content, the problem is to partition one string into k blocks, k as small as possible, and to permute them so as to obtain the other string. MCSP is NPhard, and only approximation algorithms are known. Here we show that MCSP is fixedparameter tractable in suitable parameters, so that practical instances can be efficiently solved to optimality.
Algorithms for comparing pedigree graphs
 CoRR
"... Pedigree graphs, or family trees, are typically constructed by an expensive process of examining genealogical records to determine which pairs of individuals are parent and child. New methods to automate this process take as input genetic data from a set of extant individuals and reconstruct ancest ..."
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Pedigree graphs, or family trees, are typically constructed by an expensive process of examining genealogical records to determine which pairs of individuals are parent and child. New methods to automate this process take as input genetic data from a set of extant individuals and reconstruct ancestral individuals. There is a great need to evaluate the quality of these methods by comparing the estimated pedigree to the true pedigree. In this paper, we consider two main pedigree comparison problems. The first is the pedigree isomorphism problem, for which we present a lineartime algorithm for leaflabeled pedigrees. The second is the pedigree edit distance problem, for which we present 1) several algorithms that are fast and exact in various special cases, and 2) a general, randomized heuristic algorithm. In the negative direction, we first prove that the pedigree isomorphism problem is as hard as the general graph isomorphism problem, and that the subpedigree isomorphism problem is NPhard. We then show that the pedigree edit distance problem is APXhard in general and NPhard on leaflabeled pedigrees. We use simulated pedigrees to compare our editdistance algorithms to each other as well as to a branchandbound algorithm that always finds an optimal solution.
Better Approximations for the Minimum Common Integer Partition Problem
"... Abstract. In the kMinimum Common Integer Partition Problem, abbreviated kMCIP, we are given k multisets X1,..., Xk of positive integers, and the goal is to find an integer multiset T of minimal size for which for each i, we can partition each of the integers in Xi so that the disjoint union (multi ..."
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Abstract. In the kMinimum Common Integer Partition Problem, abbreviated kMCIP, we are given k multisets X1,..., Xk of positive integers, and the goal is to find an integer multiset T of minimal size for which for each i, we can partition each of the integers in Xi so that the disjoint union (multiset union) of their partitions equals T. This problem has many applications to computational molecular biology, including ortholog assignment and fingerprint assembly. We prove better approximation ratios for kMCIP by looking at what we call the redundancy of X1,..., Xk, which is a quantity capturing the frequency of integers across the different Xi. Namely, we show.614kapproximability, improving upon the previous best known (k − 1/3)approximability for this problem. A key feature of our algorithm is that it can be implemented in almost linear time.
Hardware index to set partition converter.
 In 9th International Workshop on Applied Reconfigurable Computing (ARC2013), Proceedings Lecture Notes in Computer Science (LNCS 7806).
, 2013
"... Abstract. We demonstrate, for the first time, highspeed circuits that generate partitions on a set S of n objects. We offer two versions. In the first, partitions are produced in lexicographical order in response to successive clock pulses. In the second, an index input determines the set partitio ..."
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Abstract. We demonstrate, for the first time, highspeed circuits that generate partitions on a set S of n objects. We offer two versions. In the first, partitions are produced in lexicographical order in response to successive clock pulses. In the second, an index input determines the set partition produced. Such circuits are needed in the hardware implementation of the optimum distribution of tasks to processors. Our circuits are combinational. For large n, they can have large delay. However, one can easily pipeline them to produce one set partition per clock period. We show 1) analytical and 2) experimental time/complexity results that quantify the efficiency of our designs. Our results show that a hardware partition generator running on a 100 MHz FPGA produces partitions at a rate that is approximately 10 times the rate of a software implementation on a processor running at 2.26 GHz.
Highspeed hardware partition generation
"... We demonstrate circuits that generate set and integer partitions on a set S of n objects at a rate of one per clock. Partitions are ways to group elements of a set together and have been extensively studied by researchers in algorithm design and theory. We offer two versions of a hardware set parti ..."
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We demonstrate circuits that generate set and integer partitions on a set S of n objects at a rate of one per clock. Partitions are ways to group elements of a set together and have been extensively studied by researchers in algorithm design and theory. We offer two versions of a hardware set partition generator. In the first, partitions are produced in lexicographical order in response to successive clock pulses. In the second, an index input determines the set partition produced. Such circuits are useful in the hardware implementation of the optimum distribution of tasks to processors. We show circuits for integer partitions as well. Our circuits are combinational. For large n, they can have a large delay. However, one can easily pipeline them to produce one partition per clock period. We show (1) analytical and (2) experimental time/complexity results that quantify the efficiency of our designs. For example, our results show that a hardware set partition generator running on a 100MHz FPGA produces partitions at a rate that is approximately 10 times the rate of a software implementation on a processor running at 2.26GHz.
PROCEEDINGS Open Access Isomorphism and similarity for 2generation pedigrees
"... We consider the emerging problem of comparing the similarity between (unlabeled) pedigrees. More specifically, we focus on the simplest pedigrees, namely, the 2generation pedigrees. We show that the isomorphism testing for two 2generation pedigrees is GIhard. If the 2generation pedigrees are mon ..."
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We consider the emerging problem of comparing the similarity between (unlabeled) pedigrees. More specifically, we focus on the simplest pedigrees, namely, the 2generation pedigrees. We show that the isomorphism testing for two 2generation pedigrees is GIhard. If the 2generation pedigrees are monogamous (i.e., each individual at level1 can mate with exactly one partner) then the isomorphism testing problem can be solved in polynomial time. We then consider the problem by relaxing it into an NPcomplete decomposition problem which can be formulated as the Minimum Common Integer Pair Partition (MCIPP) problem, which we show to be FPT by exploiting a property of the optimal solution. While there is still some difficulty to overcome, this lays down a solid foundation for this research.
HighSpeed Hardware Partition Generation
, 2014
"... We demonstrate circuits that generate set and integer partitions on a set S of n objects at a rate of one per clock. Partitions are ways to group elements of a set together and have been extensively studied by researchers in algorithm design and theory. We offer two versions of a hardware set partit ..."
Abstract
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We demonstrate circuits that generate set and integer partitions on a set S of n objects at a rate of one per clock. Partitions are ways to group elements of a set together and have been extensively studied by researchers in algorithm design and theory. We offer two versions of a hardware set partition generator. In the first, partitions are produced in lexicographical order in response to successive clock pulses. In the second, an index input determines the set partition produced. Such circuits are useful in the hardware implementation of the optimum distribution of tasks to processors. We show circuits for integer partitions as well. Our circuits are combinational. For large n, they can have a large delay. However, one can easily pipeline them to produce one partition per clock period. We show (1) analytical and (2) experimental time/complexity results that quantify the efficiency of our designs. For example, our results show that a hardware set partition generator running on a 100MHz FPGA produces partitions at a rate that is approximately 10 times the rate of a software implementation on a processor running at 2.26GHz.