منابع مشابه
Permutation Reconstruction from Minors
We consider the problem of permutation reconstruction, which is a variant of graph reconstruction. Given a permutation p of length n, we delete k of its entries in each possible way to obtain (n k ) subsequences. We renumber the sequences from 1 to n−k preserving the relative size of the elements to form (n−k)-minors. These minors form a multiset Mk(p) with an underlying set M ′ k(p). We study ...
متن کاملPermutation Reconstruction from Differences
We prove that the problem of reconstructing a permutation π1, . . . , πn of the integers [1 . . . n] given the absolute differences |πi+1 − πi|, i = 1, . . . , n − 1 is NP– complete. As an intermediate step we first prove the NP–completeness of the decision version of a new puzzle game that we call Crazy Frog Puzzle. The permutation reconstruction from differences is one of the simplest combina...
متن کاملPermutation Reconstruction
In this paper, we consider the problem of permutation reconstruction. This problem is an analogue of graph reconstruction, a famous question in graph theory. In the case of permutations, the problem can be stated as follows: In all possible ways, delete k entries of the permutation p = p1p2p3...pn and renumber accordingly, creating (n k ) substrings. How large must n be in order for us to be ab...
متن کاملPermutation Reconstruction from MinMax-Betweenness Constraints
In this paper, we investigate the reconstruction of permutations on {1, 2, . . . , n} from betweenness constraints involving the minimum and the maximum element located between t and t + 1, for all t = 1, 2, . . . , n − 1. We propose two variants of the problem (directed and undirected), and focus first on the directed version, for which we draw up general features and design a polynomial algor...
متن کاملReconstructing Permutations from Identification Minors
We consider the problem whether a permutation of a finite set is uniquely determined by its identification minors. While there exist non-reconstructible permutations of every set with two, three, or four elements, we show that every permutation of a finite set with at least five elements is reconstructible from its identification minors. Moreover, we provide an algorithm for recovering a permut...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2006
ISSN: 1077-8926
DOI: 10.37236/1092