Arash Farzan

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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 problem of encoding a graph with n vertices 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 the(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 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)
We consider the problem of highly space-efficient representation of separable graphs while supporting queries in constant time in the RAM with logarithmic word size. In particular, we show constanttime support for adjacency, degree and neighborhood queries. For any monotone class of separable graphs, the storage requirement of the representation is optimal(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)
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 interested in the worst-case complexity of evaluating the expression in terms of the sizes of the sets. We assume the sets in the given expression are independent. We(More)