String matching is a classical problem in computer science. It’s essential for network content security applications, and the technique is widely applied in the pattern recognition, spelling checking, intrusion detection, worm containment, information security and so on. In this paper, a new algorithm is proposed to construct smallest suffix automaton to achieve high performance and efficient s...

Problem 1. [20 points] The adjacency matrix A of a graph G with n vertices as defined in lecture is an n×n matrix in which Ai,j is 1 if there is an edge from i to j and 0 if there is not. In lecture we saw how the smallest k where Ai,j 6= 0 describes the length of the shortest path from i to j. Given a combinatorial interpretation of the following statements about the adjacency matrix in terms ...

For any positive integer n, the Pseudo-Smarandache function Z(n) is defined as the smallest positive integer k such that n | k(k + 1) 2 . That is, Z(n) = min { k : n| + 1) 2 } . The main purpose of this paper is using the elementary methods to study the mean value properties of p(n) Z(n) , and give a sharper asymptotic formula for it, where p(n) denotes the smallest prime divisor of n.

The reciprocal complementary Wiener number of a connected graph G is defined as ( ) { } ( ) ( ) | ∑ u v V G RCW G d d u v G ⊆ = + − , 1 1 , where ( ) V G is the vertex set. ( ) | d u v G , is the distance between vertices u and v, and d is the diameter of G. A tree is known as a caterpillar if the removal of all pendant vertices makes it as a path. Otherwise, it is called a non-caterpillar. Amo...

Smallest rectilinear paths are rectilinear paths with a minimum number of bends and with a minimum length, simultaneously. In this paper, given two pairs of terminals within a rectilinear polygon, we derive an algorithm to find a pair of noncrossing rectilinear paths within the polygon such that the total number of bends and the total length are both minimized. Although a smallest rectilinear p...