In this paper, an idea for improvement of suffix array construction using lazy evaluation is presented. Evaluation of the suffix array is based on the searching queries; only the necessary part of the suffix array is built when unevaluated part of the suffix array is referred during the searching process. This is less time consuming than constructing complete suffix array. We propose lazy evaluation of Schürmann-Stoye algorithm. Experimental results show that lazy Schürmann-Stoye algorithm runs faster than Maniscalco, which is well-recognized as the fastest suffix sorting algorithm, under the constraint of small LCP (longest common prefix) and a limited number of searching queries.

In geographical databases for navigation, users raise various types of queries concerning route guidance. The most fundamental query is a shortest-route query, but, as dynamical traffic information newly becomes available and the static geographical database of roads itself has grown up further, more flexible queries are required to realize a user-friendly interface meeting the current settings. One important query among them is a detour query which provides information about detours, say listing several candidates for useful detours. This paper first reviews algorithms for the shortest and k shortest paths, and discusses their extensions to detour queries. Algorithms for finding a realistic detour are given. The efficiency and property of the algorithms are examined through experiments on an actual road network.

In this paper, we study the approximate point set matching (APSM) problem with minimum RMSD score under translation, rotation, and one-to-one correspondence in d-dimension. Since most of the previous works about APSM problems use similality scores that do not especially care about one-to-one correspondence between points, such as Hausdorff distance, we cannot easily apply previously proposed methods to our APSM problem. So, we focus on speed-up of exhaustive search algorithms that can find all approximate matches. First, we present an efficient branch-and-bound algorithm using a novel lower bound function of the minimum RMSD score for the enumeration version of APSM problem. Then, we modify this algorithm for the optimization version. Next, we present another algorithm that runs fast with high probability when a set of parameters are fixed. Experimental results on both synthetic datasets and real 3-D molecular datasets showed that our branch-and-bound algorithm achieved significant speed-up over the naive algorithm still keeping the advantage of generating all answers.

The problem of constructing the suffix tree of a tree is a generalization of the problem of constructing the suffix tree of a string. It has many applications, such as in minimizing the size of sequential transducers and in tree pattern matching. The best-known algorithm for this problem is Breslauer's O(nlog |Σ|) time algorithm where n is the size of the CS-tree and |Σ| is the alphabet size, which requires O(nlog n) time if |Σ| is large. We improve this bound by giving an optimal linear time algorithm for integer alphabets. We also describe a new data structure, the Bsuffix tree, which enables efficient query for patterns of completely balanced k-ary trees from a k-ary tree or forest. We also propose an optimal O(n) algorithm for constructing the Bsuffix tree for integer alphabets.