  Lossless data compression has been widely studied in computer science. One of
the most widely used lossless data compressions is Lempel-Zip(LZ) 77 parsing,
which achieves a high compression ratio. Bidirectional (a.k.a. macro) parsing
is a lossless data compression and computes a sequence of phrases copied from
another substring (target phrase) on either the left or the right position in
an input string. Gagie et al.(LATIN 2018) recently showed that a large gap
exists between the number of smallest bidirectional phrases of a given string
and that of LZ77 phrases. In addition, finding the smallest bidirectional parse
of a given text is NP-complete. Several variants of bidirectional parsing have
been proposed thus far, but no prior work for bidirectional parsing has
achieved high compression that is smaller than that of LZ77 phrasing for any
string. In this paper, we present the first practical bidirectional parsing
named LZ77 parsing with right reference (LZRR), in which the number of LZRR
phrases is theoretically guaranteed to be smaller than the number of LZ77
phrases. Experimental results using benchmark strings show the number of LZRR
phrases is approximately five percent smaller than that of LZ77 phrases.
