Quadratic-backtracking algorithm for string reconstruction from substring compositions

Acharya, Jayadev; Das, Hirakendu; Milenković, Olgica; Orlitsky, Alon; Pan, Shilie

doi:10.1109/isit.2014.6875042

Cited by 8 publications

(10 citation statements)

References 13 publications

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“…In this section, we study the query complexity for reconstructing an unknown length-n string, S, using jumbled-index queries. As observed by Acharya et al [1,2], strings and their reversals have the same "composition multiset". This immediately implies the following negative result, which we prove regardless for completeness.…”

Section: Jumbled-index Queriesmentioning

confidence: 66%

“…Unfortunately, for the AJI variant, there are some strings that cannot be fully reconstructed, but this is admittedly not obvious. In fact, the unreconstructability characterization of [1,2] fails for AJI queries, because the symmetry property used in their construction of pairwise "equicomposable" strings inherently yields matching substrings with symmetric (e.g. different) positions in S.…”

Section: ⊓ ⊔mentioning

confidence: 99%

“…Non-adaptive Jumbled-Index Queries In [1,2], Acharya et al study a non-adaptive version of the problem of enumerating candidate strings from the composition multiset of the underlying string. The composition multiset corresponds to the set of answers to all possible queries of the following type: given a Parikh vector, how many times does a matching substring occur in the hidden string?…”

Section: Non-adaptive Substring Queriesmentioning

confidence: 99%

“…Its time complexity is 2⌊lg n⌋ + 1. A more sophisticated version of this procedure exists (see [21]) that actually improves the time complexity into ⌊lg L (0) ⌋ + ⌊lg L (1)…”

Section: Preliminariesmentioning

confidence: 99%

“…Unfortunately, this introduces a multiplicative O(lg n) term into the query complexity. To avoid it, we show how we can take advantage of the Periodicity Lemma (1) to amortize the extra work needed to recover S.…”

Section: Uncorrupted Periodic Strings Of Unknown Sizementioning

confidence: 99%

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Adaptive Exact Learning in a Mixed-Up World: Dealing with Periodicity, Errors and Jumbled-Index Queries in String Reconstruction

Afshar¹,

Amir²,

Goodrich³

et al. 2020

Preprint

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We study the query complexity of exactly reconstructing a string from adaptive queries, such as substring, subsequence, and jumbled-index queries. Such problems have applications, e.g., in computational biology. We provide a number of new and improved bounds for exact string reconstruction for settings where either the string or the queries are "mixed-up". For example, we show that a periodic (i.e., "mixed-up") string, S = p k p ′ , of smallest period p, where |p ′ | < |p|, can be reconstructed using O(σ|p| + lg n) substring queries, where σ is the alphabet size, if n = |S| is unknown. We also show that we can reconstruct S after having been corrupted by a small number of errors d, measured by Hamming distance. In this case, we give an algorithm that uses O(dσ|p|+d|p| lg n d+1 ) queries. In addition, we show that a periodic string can be reconstructed using 2σ⌈lg n⌉ + 2|p|⌈lg σ⌉ subsequence queries, and that general strings can be reconstructed using 2σ⌈lg n⌉ + n⌈lg σ⌉ subsequence queries, without knowledge of n in advance. This latter result improves the previous best, decades-old result, by Skiena and Sundaram. Finally, we believe we are the first to study the exact-learning query complexity for string reconstruction using jumbled-index queries, which are a "mixed-up" type of query that have received much attention of late.

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Section: Jumbled-index Queriesmentioning

confidence: 66%

Section: ⊓ ⊔mentioning

confidence: 99%

Section: Non-adaptive Substring Queriesmentioning

confidence: 99%

“…Its time complexity is 2⌊lg n⌋ + 1. A more sophisticated version of this procedure exists (see [21]) that actually improves the time complexity into ⌊lg L (0) ⌋ + ⌊lg L (1)…”

Section: Preliminariesmentioning

confidence: 99%

Section: Uncorrupted Periodic Strings Of Unknown Sizementioning

confidence: 99%

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