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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
New problem results: Consecutive Block Minimization

New problem results: Consecutive Block Minimization

Layouni, Zoubir

Paperback

General Mathematics

ISBN10: 6208992176
ISBN13: 9786208992170
Publisher: Our Knowledge Publishing
Published: Jun 23 2025
Pages: 52
Weight: 0.18
Height: 0.12 Width: 6.00 Depth: 9.00
Language: English
In this book, we focus on a special property in a binary matrix, known as the 1-consecutive property. A consecutive block is a sequence of consecutively located 1s. The problem is to find a permutation of the columns so that the number of consecutive blocks in the induced matrix is minimal. We point out that it is NP-complete for general instances, then we present applications to it, variants and a state of the art. Our first contribution consists in proving that CBM is NP-complete even when the binary matrix has only two 1's per row, by polynomially transforming the maximum-weight Hamiltonian chain problem to CBM restricted to the instances in question.A second contribution consisted in solving the question: is CBM approximable with guarantee? The answer was found in the form of a polynomial heuristic that constructs permutations leading to a number of consecutive blocks within 50% of the optimum.

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