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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 propose a uniform approach for succinct representation of various families of trees. The method is based on two recursive decomposition of trees into subtrees. Recursive decomposition of a structure into substructures is a common technique in succinct data structures and has been shown fruitful in succinct representation of ordinal trees [7, 10] and… (More)

We consider the problem of encoding a graph with n ver-tices and m edges compactly supporting adjacency, neighborhood and degree queries in constant time in the log n-bit word RAM model. The adjacency query asks whether there is an edge between two vertices, the neighborhood query reports the neighbors of a given vertex in constant time per neighbor, and… (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 problem of representing and performing computations on finite abelian groups. Assuming a lg <i>n</i>-bit<sup>1</sup> word model and considering any abelian group of order <i>n</i>, we show how to represent the group in constant number of words and perform three fundamental group operations of equality testing, multiplication, and inversion… (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)

A preliminary version of this work has been published in the proceedings of International Colloquium on Automata, Languages and Programming(ICALP) 2005 [4]. Abstract. We consider the problem of evaluating an expression consisting of unions and intersections of some sorted sets in the comparison model. Given the expression and the sizes of the sets, we are… (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)