Maintaining Dynamic Sequences under Equality Tests in Polylogarithmic Time

Kurt Mehlhorn, R. Sundar, Christian Uhrig

Abstract: We present a randomized and a deterministic data structure for maintaining a dynamic family of sequences under equality tests of pairs of sequences and creations of new sequences by joining or splitting existing sequences. Both data structures support equality tests inO(1) time. The randomized version supports new sequence creations inO(log2 n) expected time wheren is the length of the sequence created. The deterministic solution supports sequence creations inO(logn(logmlog* m+logn)) time for themth operation.