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On the minimum common integer partition problem

Xin Chen, Lan Liu, Zheng Liu, Tao Jiang
2008 ACM Transactions on Algorithms  
The MCIP problem is thus defined as to find a common integer partition of S1, · · · , S k with the minimum cardinality.  ...  We introduce a new combinatorial optimization problem in this paper, called the Minimum Common Integer Partition (MCIP) problem, which was inspired by computational biology applications including ortholog  ...  This project is supported in part by NSF grants CCR-0309902 and DBI-0133265, NSFC grant 60528001, National Key Project for Basic Research (973) grant 2002CB512801, and a fellowship from the Center for  ... 
doi:10.1145/1435375.1435387 fatcat:u2aahzmxffgrtnlqf5d6wyr2y4

On the Minimum Common Integer Partition Problem [chapter]

Xin Chen, Lan Liu, Zheng Liu, Tao Jiang
2006 Lecture Notes in Computer Science  
The MCIP problem is thus defined as to find a common integer partition of S1, · · · , S k with the minimum cardinality.  ...  We introduce a new combinatorial optimization problem in this paper, called the Minimum Common Integer Partition (MCIP) problem, which was inspired by computational biology applications including ortholog  ...  This project is supported in part by NSF grants CCR-0309902 and DBI-0133265, NSFC grant 60528001, National Key Project for Basic Research (973) grant 2002CB512801, and a fellowship from the Center for  ... 
doi:10.1007/11758471_24 fatcat:ywiqccfz2jbvldf2ueti7vzvni

An Integer Programming Formulation of the Minimum Common String Partition Problem

S. M. Ferdous, M. Sohel Rahman, Lars Kaderali
2015 PLoS ONE  
We consider the problem of finding a minimum common partition of two strings (MCSP). The problem has its application in genome comparison. MCSP problem is proved to be NP-hard.  ...  In this paper, we develop an Integer Programming (IP) formulation for the problem and implement it.  ...  Acknowledgments One of the authors, M. Sohel Rahman is currently on a sabbatical leave from Bangladesh University of Engineering and Technology (BUET). Author Contributions  ... 
doi:10.1371/journal.pone.0130266 pmid:26134848 pmcid:PMC4489654 fatcat:txh5byohzbc3zen6b6lmdbytoy

Isomorphism and similarity for 2-generation pedigrees

Haitao Jiang, Guohui Lin, Weitian Tong, Daming Zhu, Binhai Zhu
2015 BMC Bioinformatics  
We then consider the problem by relaxing it into an NP-complete decomposition problem which can be formulated as the Minimum Common Integer Pair Partition (MCIPP) problem, which we show to be FPT by exploiting  ...  We consider the emerging problem of comparing the similarity between (unlabeled) pedigrees. More specifically, we focus on the simplest pedigrees, namely, the 2-generation pedigrees.  ...  We then relax the similarity measure and formulate this as a Minimum Common Integer Pair Partition (MCIPP) problem, generalizing the famous NP-complete Minimum Common Integer Partition (MCIP) problem,  ... 
doi:10.1186/1471-2105-16-s5-s7 pmid:25860335 pmcid:PMC4402698 fatcat:my36ch4yv5as3n3dq573b6a3c4

Better Approximations for the Minimum Common Integer Partition Problem [chapter]

David P. Woodruff
2006 Lecture Notes in Computer Science  
In the k-Minimum Common Integer Partition Problem, abbreviated k-MCIP, we are given k multisets X1, . . . , X k of positive integers, and the goal is to find an integer multiset T of minimal size for which  ...  Keywords: minimum common integer partition problem, approximation algorithms, computational biology The author would like to thank Andrew Yao and Tsinghua University for hospitality and support while performing  ...  We have given an O(m log k)-time algorithm for k-MCIP with approximation ratio .614k, improving the previous bound of k − 1/3. The best lower bound is Ω(1).  ... 
doi:10.1007/11830924_24 fatcat:wxm6o7xowvfxvnvdsb4m3ejvcy

Minimum common string partition revisited

Haitao Jiang, Binhai Zhu, Daming Zhu, Hong Zhu
2010 Journal of combinatorial optimization  
Minimum Common String Partition (MCSP) has drawn much attention due to its application in genome rearrangement.  ...  d; and x-balanced MCSP, which requires the length of blocks being in range (n/k − x, n/k + x), where n is the length of the input strings, k is the number of blocks in the optimal common partition and  ...  The minimum common string partition problem is to compute a common partition of X and Y with the minimum number of blocks.  ... 
doi:10.1007/s10878-010-9370-2 fatcat:2eqp7fzjhrd4pexqc4cusetlkm

Minimum Common String Partition Revisited [chapter]

Haitao Jiang, Binhai Zhu, Daming Zhu, Hong Zhu
2010 Lecture Notes in Computer Science  
Minimum Common String Partition (MCSP) has drawn much attention due to its application in genome rearrangement.  ...  d; and x-balanced MCSP, which requires the length of blocks being in range (n/k − x, n/k + x), where n is the length of the input strings, k is the number of blocks in the optimal common partition and  ...  The minimum common string partition problem is to compute a common partition of X and Y with the minimum number of blocks.  ... 
doi:10.1007/978-3-642-14553-7_7 fatcat:nyeaojyymrdf3icc7vlex5frca

A network flow approach to the Minimum Common Integer Partition Problem

Wenbo Zhao, Peng Zhang, Tao Jiang
2006 Theoretical Computer Science  
In the k-Minimum Common Integer Partition Problem, abbreviated as k-MCIP, we are given k multisets X 1 , . . . , X k of positive integers, the goal is to find an integer multiset T of the minimum size  ...  such that for every i, we can partition each of the integers in X i so that the disjoint (multiset) union of their partitions equals T.  ...  Woodruff for his comments on an earlier draft of this paper.  ... 
doi:10.1016/j.tcs.2006.09.001 fatcat:5x36f4hwgve4lfpyyvfwz3ugrm

Reversal Distance for Strings with Duplicates: Linear Time Approximation Using Hitting Set [chapter]

Petr Kolman, Tomasz Waleń
2007 Lecture Notes in Computer Science  
Particular attention has been given to the problem of sorting by reversals (SBR): given two strings, A and B, find the minimum number of reversals that transform the string A into the string B (a reversal  ...  In the last decade there has been an ongoing interest in string comparison problems; to a large extend the interest was stimulated by genome rearrangement problems in computational biology but related  ...  A challenging open question is whether it is possible to get a nontrivial approximation ratio independent of the parameter k (or at least less dependent, say an approximation ratio O(log k)).  ... 
doi:10.1007/11970125_22 fatcat:jz5y7aw4jjhzbnqq5z6np7nyny

A Self-Tuning Procedure for Resource Management in InterCloud Computing

Suleiman Onimisi Aliyu, Feng Chen, Han Li
2016 2016 IEEE International Conference on Software Quality, Reliability and Security Companion (QRS-C)  
Essentially, this paper presents an Integer partition based anytime algorithm as an optimal cost solution to the bi-objective optimisation problem in resource management; anchored principally on practical  ...  The space of cooperative arrangements (resource sharing) between the participant cloud systems is presented by using Integer Partitioning to characterise the worst case communication complexity in peer  ...  resource coalition sizes in common and so on.  ... 
doi:10.1109/qrs-c.2016.50 dblp:conf/qrs/AliyuCL16 fatcat:gbgo5gkzvfhw3gofic6nx7k7im

Rectangle Transformation Problem [article]

Shaojiang Wang, Kun He, Yicheng Pan, Mingji Xia
2017 arXiv   pre-print
We are interested in the minimum RTP which requires to minimize the partition size.  ...  We mainly focus on the strict rectangle transformation problem (SRTP) in which rotation is not allowed in transforming.  ...  Guessing the patterns and the one-one map for the isomorphic rectangle partitions implies that the deterministic versions of minimum IRTP and minimum SIRTP with integral solution restriction are just both  ... 
arXiv:1710.10924v1 fatcat:bxruua2q2fdgxaqjjrnvslz4ie

The minimum weight t-composition of an integer

D. M. Cardoso, J. O. Cerdeira
2012 Journal of Mathematical Sciences  
This study was motivated by a problem arising from the automobile industry, and the presented result is useful when dealing with huge location problems.  ...  We show that finding a minimum weight t-composition of p reduces to the determination of a shortest path in a certain digraph with O(tp) vertices.  ...  The quality of the solution depends, on one hand, on the way the problem is splitted into t sub-problems and, on the other hand, on which solution, among the different cardinality solutions produced in  ... 
doi:10.1007/s10958-012-0741-3 fatcat:l5v66wg66nbm5eolssbolgoko4

Computational performance evaluation of two integer linear programming models for the minimum common string partition problem

Christian Blum, Günther R. Raidl
2015 Optimization Letters  
In the minimum common string partition (MCSP) problem two related input strings are given.  ...  The MCSP seeks a minimum cardinality partitioning of one string into non-overlapping substrings that is also a valid partitioning for the second string.  ...  Blum acknowledges support by grant TIN2012-37930-02 of the Spanish Government. In addition, support is acknowledged from IKERBASQUE (Basque Foundation for Science). Our  ... 
doi:10.1007/s11590-015-0921-4 fatcat:mrsnvxybjzfcpovsc2nmef2udm

Task period selection to minimize hyperperiod

Vicent Brocal, Patricia Balbastre, Rafael Ballester, Ismael Ripoll
2011 ETFA2011  
A new algorithm, which allows to calculate the minimum hyperperiod of such a set of tasks, is presented.  ...  This algorithm calculates the minimum value even with a large number of tasks, where exhaustive search becomes intractable.  ...  continue improving the presented algorithm as well as possibly developing new ones.  ... 
doi:10.1109/etfa.2011.6059178 dblp:conf/etfa/BrocalBBR11 fatcat:elvkjbqc75aujn34piqqjh2udq

The complexity of greatest common divisor computations [chapter]

Bohdan S. Majewski, George Havas
1994 Lecture Notes in Computer Science  
We study the complexity of expressing the greatest common divisor of n positive numbers as a linear combination of the numbers.  ...  We present and analyze a new method for expressing the gcd of n numbers as their linear combination and give an upper bound on the size of the largest multiplier produced by this method, which is optimal  ...  We start with the following problem: MINIMUM GCD SET INSTANCE: Multiset A of positive integers, positive integer K ≤ |A|.  ... 
doi:10.1007/3-540-58691-1_56 fatcat:sztewni7p5ekphf5aizfwsncfe
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