Improved string matching with k mismatches
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Recently, an efficient algorithm for such a problem has been devised by [2] . Its time performance i s 0(k(mlogm+n)) and it uses 0(k(m+n)) space. Here we present a compact version of their algorithm , achieving a time performance of 0(mlogm+kn) for general alphabets and of 0(m+kn) for alphabet s whose size is fixed . Our algorithm uses 0(m) space. The data structure that we use is the suffix tree [1] o f the pattern modified in order to support the static lowest common ancestor algorithm (LCA for short) given in [5] . In more recent versions of [2] the authors used the suffix tree for the problem of strin g matching with k differences [4] but not for the problem of string matching with k mismatches [3] .
[1] Gad M. Landau,et al. Efficient String Matching with k Mismatches , 2018, Theor. Comput. Sci..
[2] Peter Weiner,et al. Linear Pattern Matching Algorithms , 1973, SWAT.
[3] Robert E. Tarjan,et al. Fast Algorithms for Finding Nearest Common Ancestors , 1984, SIAM J. Comput..
[4] Gad M. Landau,et al. Efficient string matching in the presence of errors , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).