Learn More
We propose a uniform method to encode various types of trees succinctly. These families include ordered (ordinal), k-ary (cardinal), and unordered (free) trees. We will show the approach is intrinsically suitable for obtaining entropy-based encodings of trees (such as the degree-distribution entropy). Previously-existing succinct encodings of trees use ad(More)
We investigate the problem of finding an unknown cut through querying vertices of a graph G. Our complexity measure is the number of submitted queries. To avoid some worst cases, we make a few assumptions which allow us to obtain an algorithm with the worst case query complexity of O(k) + 2k log n k in which k is the number of vertices adjacent to(More)
We consider the succinct representation of ordinal and cardinal trees on the RAM with logarithmic word size. Given a tree T , our representations support the following operations in O(1) time: (i) BP-substring(i, b), which reports the substring of length b bits (b is at most the wordsize) beginning at position i of the balanced parenthesis representation of(More)
INTRODUCTION In this study, we aimed to measure the inclination of teeth on dental casts by a manual technique with the tooth inclination protractor (TIP; MBI, Newport, United Kingdom) and a newly designed 3-dimensional (3D) software program. The correlation of the 2 techniques was evaluated, and the reliability of each technique was assessed separately. (More)
We give the first fully compressed representation of a set of m points on an n×n grid, taking H +o(H) bits of space, where H = lg n 2 m is the entropy of the set. This representation supports range counting, range reporting, and point selection queries, with a performance that is comparable to that of uncompressed structures and that improves upon the only(More)
Given an unlabeled, unweighted, and undirected graph with n vertices and small (but not necessarily constant) treewidth k, we consider the problem of preprocessing the graph to build space-efficient encodings (oracles) to perform various queries efficiently. We assume the word RAM model where the size of a word is Ω(logn) bits. The first oracle, we present,(More)