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Approximating Optimal Bidirectional Macro Schemes

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Luís Russo, Ana Correia, Gonzalo Navarro, and Alexandre Francisco

Lempel-Ziv is an easy-to-compute member of a wide family of so-called macro
schemes;
it restricts pointers to go in one direction only. Optimal bidirectional macro
schemes are
NP-complete to find, but they may provide much better compression on highly
repetitive
sequences. We consider the problem of approximating optimal bidirectional
macro schemes.
We describe a simulated annealing algorithm that usually, in a few iterations,
converges to
a 2-approximation of the optimal bidirectional macro scheme. We test our
algorithm on a
number of real and artificial repetitive texts and verify that it is efficient
in practice and
outperforms Lempel-Ziv, sometimes by a wide margin.