An O ( n log n ) Algorithm for nding
نویسندگان
چکیده
Let be a nite alphabet and x 2 n. A string y 2 m is said to be k-dissimilar to x, if no k length substring of x is equal to any k length substring of y. We present an O(n log n) algorithm which on input x 2 n and an integer m n outputs an integer k and y 2 m such that: y is k-dissimilar to x. There does not exist a string z of length m which is k ? 1 dissimilar to x.
منابع مشابه
Ultrafast Randomized Parallel Construction and Approximation Algorithms for Spanning Forests in Dense Graphs
We present a rst randomized O(log n) time and O(n+m) work CRCWPRAM algorithm for nding a spanning forest of an undirected dense graph with n vertices. Furthermore we construct a randomized O(log log n) time and O(n log n) work CREW-PRAM algorithm for nding spanning trees in random graphs.
متن کاملParallel Algorithm for the Matrix Chain Product and the Optimal Triangulation Problems Stacs'93 Version
This paper considers the problem of nding an optimal order of the multiplication chain of matrices and the problem of nding an optimal triangulation of a convex polygon. For both these problems the best sequential algorithms run in (n log n) time. All parallel algorithms known use the dynamic programming paradigm and run in a polylogarithmic time using, in the best case, O(n 6 =log k n) process...
متن کاملRectilinear Path Problems among Rectilinear Obstacles Revisited
We present eecient algorithms for nding rectilinear collision-free paths between two given points among a set of rectilinear obstacles. Our results improve the time complexity of previous results for nding the shortest rectilinear path, the minimum-bend shortest rectilinear path, the shortest minimum-bend rectilinear path and the minimum-cost rectilinear path. For nding the shortest rectilinear...
متن کاملOptimal Randomized EREW PRAM Algorithms for Finding Spanning Forests
We present the rst randomized O(log n) time and O(m+n) work EREW PRAM algorithm for nding a spanning forest of an undirected graph G = (V; E) with n vertices and m edges. Our algorithm is optimal with respect to time, work and space. As a consequence we get optimal randomized EREW PRAM algorithms for other basic connectivity problems such as nding a bipartite partition, nding bridges and biconn...
متن کاملAn E cient Algorithm for Euclidean Shortest Path with Polygonal Obstacles
In this paper we present an e cient solution to nding the Euclidean Shortest Path from one point to the other in the presence of polygonal obstacles. An O(m 2 logn+T ) algorithm is developed where m is the number of obstacles and n, the number of vertices and T is the time for triangulation. The algorithm works by nding a restricted visibility graph in the obstacle space and is simple. It achie...
متن کاملDraft: Eecient Algorithm for Nding Two Largest Empty Circles
This paper considers the problem of nding of 2 largest equal-radius non-overlapping circles in a simple polygon. We present O(n log 3 n) algorithm for nding disks in a polygon with n vertices. It improves recent algorithm of Bield et al. 1] that takes at least (n 2) time.
متن کامل