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Reconstruction of two-valued matrices from their two projections

✍ Scribed by J. H. B. Kemperman; A. Kuba

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
120 KB
Volume
9
Category
Article
ISSN
0899-9457

No coin nor oath required. For personal study only.

✦ Synopsis

A matrix is said to be two-valued if its elements assume unknown subset S of Q from the following two projections of its at most two different values. We studied the problem of recondensity function g(i, j) on M 1 N: structing a two-valued matrix from its marginals-that is, from its row sums and column sums-but without any knowledge of the value pair on hand. Provided at least one of these marginals is nonconstant,

only finitely many (though possibly many) value pairs can lead to a valid reconstruction. Our considerations lead to an efficient algorithm

(

for calculating all possible solutions, each with its own value pair. Special attention is given to uniqueness pairs-that is, value pairs to which there corresponds precisely one matrix having the correct Here, marginals. Unless both marginals are constant, there can be no more than two uniqueness pairs.

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