Consecutive block minimization is 1.5-approximable

Haddadi, Salim; Layouni, Zoubir

doi:10.1016/j.ipl.2008.04.009

Cited by 16 publications

(13 citation statements)

References 12 publications

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“…Haddadi and others found a polynomial-time local-improvement heuristic for the CBM. They introduced two ( ) size local neighborhood search, where the blocks number of a neighbor is provided in ( ) operations [2,3].…”

Section: Polynomial-time Local-improvement Heuristic For Cbmmentioning

confidence: 99%

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A Metaheuristic Approach to the C1S Problem

Abo-Alsabeh

Salhi

2021

eijs

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Given a binary matrix, finding the maximum set of columns such that the resulting submatrix has the Consecutive Ones Property (C1P) is called the Consecutive Ones Submatrix (C1S) problem. There are solution approaches for it, but there is also a room for improvement. Moreover, most of the studies of the problem use exact solution methods. We propose an evolutionary approach to solve the problem. We also suggest a related problem to C1S, which is the Consecutive Blocks Minimization (CBM). The algorithm is then performed on real-world and randomly generated matrices of the set covering type.

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Section: Polynomial-time Local-improvement Heuristic For Cbmmentioning

confidence: 99%

“…1.1 Basic concepts of C1P and C1S Definition 1.1. A block of 1's (block of 0's) in a binary matrix A is any maximal set of consecutive one entries (zero entries) appearing in the same row [2]. A binary matrix A is said to have the Consecutive Ones Property (C1P) if the ones in every row appear consecutively [3].…”

Section: Introductionmentioning

confidence: 99%

A Metaheuristic Approach to the C1S Problem

Abo-Alsabeh

Salhi

2021

eijs

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“…CBM is NP-hard even when restricted to binary matrices having two 1s per row (Haddadi 2002). Haddadi and Layouni (2008) converted CBM to traveling salesman problem (TSP) satisfying the triangle inequality. Since this polynomial-time transformation is approximation preserving, the Christofides heuristic constitutes a 0.5-approximation for CBM.…”

Section: Preprocessingmentioning

confidence: 99%

Benders decomposition for set covering problems

Haddadi

2015

J Comb Optim

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This paper describes Benders decomposition approaches to optimally solve set covering problems " almost" satisfying the consecutive ones property. The decompositions are based on the fact that set covering problems with consecutive ones property have totally unimodular coefficient matrices. Given a binary matrix, a totally unimodular matrix is enforced by filling up every row with ones between its first and its last non-zero entries. The resulting mistake is handled by introducing additional integer variables whose number depends on the reordering of the columns of the given matrix. This leads us to consider the consecutive block minimization problem. Two cutting plane algorithms are proposed and run on a large set of benchmark instances. The results obtained show that the cutting plane algorithms outperform an existing tree search method designed exclusively for such instances.

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“…Both problems, in their decision version, have been proved in [17] to be N P-complete (a 1.5 approximation algorithm for the block minimization problem is described in [18]). For example the c1p instance where R = {a, b, c, d} and F = {{a, b, c}, {a, c, d}, {b, d}} has no solution.…”

Section: Related Workmentioning

confidence: 99%

“…Genes that appear together consistently across genomes, possibly not always in the same order, are believed to be functionally related. They often code interacting proteins and have a common functional association [19][20][21].…”

Section: Related Workmentioning

confidence: 99%

Consecutive ones property and PQ-trees for multisets: Hardness of counting their orderings

Battaglia

Grossi

Scutellí³

2012

Information and Computation

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A binary matrix satisfies the consecutive ones property (c1p) if its columns can be permuted such that the 1s in each row of the resulting matrix are consecutive. Equivalently, a family of setsF={Q1,…,Qm}, where Qi⊆R for some universe R, satisfies the c1p if the symbols in R can be permuted such that the elements of each set Qi∈F occur consecutively, as a contiguous segment of the permutation of Rʼs symbols. Motivated by combinatorial problems on sequences with repeated symbols, we consider the c1p version on multisets and prove that counting the orderings (permutations) thus generated is #P-complete. We prove completeness results also for counting the permutations generated by PQ-trees (which are related to the c1p), thus showing that a polynomial-time algorithm is unlikely to exist when dealing with multisets and sequences with repeated symbols. To prove our results, we use a combinatorial approach based on parsimonious reductions from the Hamiltonian path problem, which enables us to prove also the hardness of approximation for these counting problems

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Consecutive block minimization is 1.5-approximable

Cited by 16 publications

References 12 publications

A Metaheuristic Approach to the C1S Problem

A Metaheuristic Approach to the C1S Problem

Benders decomposition for set covering problems

Consecutive ones property and PQ-trees for multisets: Hardness of counting their orderings

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