97 research outputs found
Hardness of Detecting Abelian and Additive Square Factors in Strings
We prove 3SUM-hardness (no strongly subquadratic-time algorithm, assuming the
3SUM conjecture) of several problems related to finding Abelian square and
additive square factors in a string. In particular, we conclude conditional
optimality of the state-of-the-art algorithms for finding such factors.
Overall, we show 3SUM-hardness of (a) detecting an Abelian square factor of
an odd half-length, (b) computing centers of all Abelian square factors, (c)
detecting an additive square factor in a length- string of integers of
magnitude , and (d) a problem of computing a double 3-term
arithmetic progression (i.e., finding indices such that
) in a sequence of integers of
magnitude .
Problem (d) is essentially a convolution version of the AVERAGE problem that
was proposed in a manuscript of Erickson. We obtain a conditional lower bound
for it with the aid of techniques recently developed by Dudek et al. [STOC
2020]. Problem (d) immediately reduces to problem (c) and is a step in
reductions to problems (a) and (b). In conditional lower bounds for problems
(a) and (b) we apply an encoding of Amir et al. [ICALP 2014] and extend it
using several string gadgets that include arbitrarily long Abelian-square-free
strings.
Our reductions also imply conditional lower bounds for detecting Abelian
squares in strings over a constant-sized alphabet. We also show a subquadratic
upper bound in this case, applying a result of Chan and Lewenstein [STOC 2015].Comment: Accepted to ESA 202
Conferences WORDS, years 1997-2017: Open Problems and Conjectures
International audienceIn connection with the development of the field of Combinatorics on Words, we present a list of open problems and conjectures which were stated in the context of the eleven international meetings WORDS, which held from 1997 to 2017
The palindromization map
The palindromization map has been defined initially by Aldo de Luca in the
context of Sturmian words. It was extended to the free group of rank by
Kassel and the second autho We extend their construction to arbitrary
alphabets. We also
investigate the suffix automaton and compact suffix automaton of the words
obtained by palindromization
28th Annual Symposium on Combinatorial Pattern Matching : CPM 2017, July 4-6, 2017, Warsaw, Poland
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