3 research outputs found
A New Algebraic Approach for String Reconstruction from Substring Compositions
We consider the problem of binary string reconstruction from the multiset of
its substring compositions, i.e., referred to as the substring composition
multiset, first introduced and studied by Acharya et al. We introduce a new
algorithm for the problem of string reconstruction from its substring
composition multiset which relies on the algebraic properties of the equivalent
bivariate polynomial formulation of the problem. We then characterize specific
algebraic conditions for the binary string to be reconstructed that guarantee
the algorithm does not require any backtracking through the reconstruction,
and, consequently, the time complexity is bounded polynomially. More
specifically, in the case of no backtracking, our algorithm has a time
complexity of compared to the algorithm by Acharya et al., which has a
time complexity of , where is the length of the binary
string. Furthermore, it is shown that larger sets of binary strings are
uniquely reconstructable by the new algorithm and without the need for
backtracking leading to codebooks of reconstruction codes that are larger, by a
linear factor in size, compared to the previously known construction by
Pattabiraman et al., while having reconstruction complexity
Repeat-Free Codes
In this paper we consider the problem of encoding data into repeat-free
sequences in which sequences are imposed to contain any -tuple at most once
(for predefined ). First, the capacity and redundancy of the repeat-free
constraint are calculated. Then, an efficient algorithm, which uses a single
bit of redundancy, is presented to encode length- sequences for . This algorithm is then improved to support any value of of the form
, for , while its redundancy is . We also calculate the
capacity of repeat-free sequences when combined with local constraints which
are given by a constrained system, and the capacity of multi-dimensional
repeat-free codes.Comment: 18 page