Shiloach, Y., Fast canonization of circular strings, J. of Algorithms 2 (1981) 107121.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... Q, performing contour matching (called coastline matching in [96] and similarity scaling (by deleting the lengths y i s from string(Q) With an analogous trick, we can partition a set of polygons into equivalence classes of similar polygons, or detect similarity between two polygons (see also [19, 90]) We now mention the generalization of the suffix tree for parameterized pattern matching of Baker [13] which gives an important application in software maintenance. The problem consists of finding duplications of code in large software systems, by tracking down matches between different ....

Shiloach, Y., Fast canonization of circular strings, J. of Algorithms 2 (1981) 107121.

....as in Lemma 7 else d = 4 13. if G[x,d,i] is Exception B then link CYCLE(yi,d 1,1) and vertex as in Lemma 8 14. else link CYCLE(yi,d 1,1) with CYCLE(x,d,i 1) as in Lemma 7 Recall that L(n) is the set of lexicographically smallest representatives of the n bit necklaces. It is shown in [Shi] that for an arbitrary n bit string, x, it is possible to check whether x 2 L(n) in time O(n) Using this fact, we show that all the tests in the CYCLE algorithm can be made in time O(n) First note that by definition of r(x; d) and Corollary 1(a) r(x; d) t if and only if u(y t ; d Gamma 1) 2 ....

.... Using this fact, we show that all the tests in the CYCLE algorithm can be made in time O(n) First note that by definition of r(x; d) and Corollary 1(a) r(x; d) t if and only if u(y t ; d Gamma 1) 2 L(n) so the tests on lines (3) and (6) can be made in time O(n) using 27 the algorithm of [Shi]. By Corollary 1(a) G n [x; d; i] is empty if u(y i ; d Gamma 1) 62 L(n) and is trivial if and only if u(y i ; d Gamma 1) 2 L(n) but v(y i ; d Gamma 1) 62 L(n) By Corollary 1(b) and Lemma 2(iii) G n [x; d; i] has only two vertices if and only if v(y i ; d Gamma 1) 2 L(n) but w(y i ; d ....

Y. Shiloach "Fast canonization of circular strings" Journal of Algorithms 2, 2 (1981) 107-121.

....values of i 2 [1; n] for which X[i; i n Gamma 1] is lexicographically least. Here we state the problem in terms of W 2 merely to avoid introducing arithmetic modulo n; all the algorithms discussed here actually work on W rather than X. Such values of i will be called, following Shiloach [S81], minimum starting points (MSPs) Let us say that W has index k if W contains k MSPs but not k 1. Then the following lemma is easily proved by induction on k: Lemma 4.1 A word W of length n has index k 1 if and only if k is the largest integer for which W is a repetition of multiplicity k. ....

....canonization algorithm with unchanged asymptotic time and space complexity. As noted above, three algorithms for the canonization problem have already been published. These algorithms are strikingly different: the first [B80] is a variant of the failure function algorithm [KMP77] a second [S81] is based on a sieve technique which eliminates positions in W that cannot be MSPs; and the third [D83] is as we have seen essentially a Lyndon decomposition algorithm. Table 4.1 compares the four known canonization algorithms in terms of their use of space and time. The space measure given is in ....

Y. Shiloach, Fast canonization of circular strings, J. Algorithms 2 (1981) 107-121.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC