Compressing Probability Distributions

We show how to store good approximations of probability distributions in small space

Optimal binary trees with height restrictions on left and right branches

We begin with background definitions on binary trees. Then we review known algorithms for finding optimal binary search trees. Knuth\u27s famous algorithm, presented in the second chapter, is the cornerstone for our work. It depends on two important results: the Quadrangle Lemma and the Monoticity Theorem. These enabled Knuth to achieve a time complexity of O(n2), while previous algorithms had been O(n3) (n = size of input). We present the known generalization of Knuth\u27s algorithm to trees with a height restriction. Finally, we consider the previously unexamined case of trees with different restrictions on left and right heights. We prove the Quadrangle Lemma and the Monoticity Theorem in this case, and present an algorithm based on this

Optimizing Trees for Static Searchable Encryption

Searchable symmetric encryption (SSE) enables data owners to conduct searches over encrypted data stored by an untrusted server, retrieving only those encrypted files that match the search queries. Several recent schemes employ a server-side encrypted index in the form of a search tree where each node stores a bit vector denoting for each keyword whether any file in its subtree contains that keyword. Our work is motivated by the observation that the way data is distributed in such a search tree has a big impact on the cost of searches. For single-keyword queries, it impacts the number of different paths that must be followed to find all the matching files; for multi-keyword queries, the arrangement of the tree also impacts the number of nodes visited during the search on paths that do not lead to any satisfying data elements. We present three algorithms that improve the performance of SSE schemes based on tree indexes and prove that for cases where the search cost is high, the cost of our algorithms converges to the cost of the optimal tree. In our experiments, the resulting search trees outperform the arbitrary search trees used in previous works by a factor of up to tw