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On the minimum common integer partition problem

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 ...

##
###
On the Minimum Common Integer Partition Problem
[chapter]

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 ...

##
###
An Integer Programming Formulation of the Minimum Common String Partition Problem

2015
*
PLoS ONE
*

We consider

doi:10.1371/journal.pone.0130266
pmid:26134848
pmcid:PMC4489654
fatcat:txh5byohzbc3zen6b6lmdbytoy
*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 ...##
###
Isomorphism and similarity for 2-generation pedigrees

2015
*
BMC Bioinformatics
*

We then consider

doi:10.1186/1471-2105-16-s5-s7
pmid:25860335
pmcid:PMC4402698
fatcat:my36ch4yv5as3n3dq573b6a3c4
*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*, ...##
###
Better Approximations for the Minimum Common Integer Partition Problem
[chapter]

2006
*
Lecture Notes in Computer Science
*

In

doi:10.1007/11830924_24
fatcat:wxm6o7xowvfxvnvdsb4m3ejvcy
*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). ...##
###
Minimum common string partition revisited

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. ...

##
###
Minimum Common String Partition Revisited
[chapter]

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. ...

##
###
A network flow approach to the Minimum Common Integer Partition Problem

2006
*
Theoretical Computer Science
*

In

doi:10.1016/j.tcs.2006.09.001
fatcat:5x36f4hwgve4lfpyyvfwz3ugrm
*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. ...##
###
Reversal Distance for Strings with Duplicates: Linear Time Approximation Using Hitting Set
[chapter]

2007
*
Lecture Notes in Computer Science
*

Particular attention has been given to

doi:10.1007/11970125_22
fatcat:jz5y7aw4jjhzbnqq5z6np7nyny
*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)). ...##
###
A Self-Tuning Procedure for Resource Management in InterCloud Computing

2016
*
2016 IEEE International Conference on Software Quality, Reliability and Security Companion (QRS-C)
*

Essentially, this paper presents an

doi:10.1109/qrs-c.2016.50
dblp:conf/qrs/AliyuCL16
fatcat:gbgo5gkzvfhw3gofic6nx7k7im
*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*. ...##
###
Rectangle Transformation Problem
[article]

2017
*
arXiv
*
pre-print

We are interested in

arXiv:1710.10924v1
fatcat:bxruua2q2fdgxaqjjrnvslz4ie
*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 ...##
###
The minimum weight t-composition of an integer

2012
*
Journal of Mathematical Sciences
*

This study was motivated by a

doi:10.1007/s10958-012-0741-3
fatcat:l5v66wg66nbm5eolssbolgoko4
*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 ...##
###
Computational performance evaluation of two integer linear programming models for the minimum common string partition problem

2015
*
Optimization Letters
*

In

doi:10.1007/s11590-015-0921-4
fatcat:mrsnvxybjzfcpovsc2nmef2udm
*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 ...##
###
Task period selection to minimize hyperperiod

2011
*
ETFA2011
*

A new algorithm, which allows to calculate

doi:10.1109/etfa.2011.6059178
dblp:conf/etfa/BrocalBBR11
fatcat:elvkjbqc75aujn34piqqjh2udq
*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*. ...##
###
The complexity of greatest common divisor computations
[chapter]

1994
*
Lecture Notes in Computer Science
*

We study

doi:10.1007/3-540-58691-1_56
fatcat:sztewni7p5ekphf5aizfwsncfe
*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|. ...
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