Sharing the components of transposition-invariant distance, DIT, on DIT-organized Burkhard-Keller structure in searches for best matching strings

In this work various construction character/frequency information sharing structure approaches are proposed in order to optimize transposition_invariant distance evaluation, [SD87], that distance is used to construct a Burkhard-keller tree, [BK73] and [NK82], where is organized a dictionary of strings token over a characters alphabet [SP88], to achieve searchings of strings best matching one on Levenshtein sense [LE66]. 0.-INTRODUCTION: This work is on the line of optimizing search schemes for the strings best matching one and data structures standing them. Given a strings dictionary, a distance defined on the strings space and a search string (belonging or not to the dictionary) the question is to find all strings at minimum distance of the searching string. The aim of this work is to organize the character/frequency information from the dictionary strings in such a way that it becomes possible to improve the transposition_invariant distance evaluation, using former evaluations by means of sharing the character/frequency information with different strings. In section 1 the distance used is the directional distance, DD, introduced by Levenshtein, [LE66], evaluated by Wagner and Fisher, [WF74], and whose optimized evaluation algorithm is described in [SP88]. In section 2 appears a Transposition_Invariant distance, DIT, with a lower cost than DD, which is used as an adaptive filter to searchings [SD87]. DITE+DD search scheme [SD87] is described in section 3. Section 4 discusses BK_DIT+DD search scheme [SP88] achieved over a Burkhard and Keller (BK) tree structure, [BK73] and [NK82]. DIT components sharing structure is studied in section 5. In section 6 various construction approaches for that structure are proposed. Section 7 suggests an approach for the BK tree construction according to the sharing structure. Section 8 shows experimental results and conclusions of this work. µ, the nil string. ³ ³X³ ³ is the length of X. An editing operation is a pair (ß,Ω Ω)=,/(µ µ,µ µ), where ß and Ω Ω are strings of length less or equal than one, i. e., they are µ µ or they are a single character. String Y results of the application of (ß,Ω Ω) on X if X=σ σßΦ Φ and Y=σΩΦ σΩΦ, that is written X->Y.