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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 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)
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)