Theory and Techniques for Synthesizing a Family of Graph Algorithms

Although Breadth-First Search (BFS) has several advantages over Depth-First Search (DFS) its prohibitive space requirements have meant that algorithm designers often pass it over in favor of DFS. To address this shortcoming, we introduce a theory of Efficient BFS (EBFS) along with a simple recursive program schema for carrying out the search. The theory is based on dominance relations, a long standing technique from the field of search algorithms. We show how the theory can be used to systematically derive solutions to two graph algorithms, namely the Single Source Shortest Path problem and the Minimum Spanning Tree problem. The solutions are found by making small systematic changes to the derivation, revealing the connections between the two problems which are often obscured in textbook presentations of them.Comment: In Proceedings SYNT 2012, arXiv:1207.055

Speeding-up qq-gram mining on grammar-based compressed texts

We present an efficient algorithm for calculating $q$-gram frequencies on strings represented in compressed form, namely, as a straight line program (SLP). Given an SLP $\mathcal{T}$ of size $n$ that represents string $T$, the algorithm computes the occurrence frequencies of all $q$-grams in $T$, by reducing the problem to the weighted $q$-gram frequencies problem on a trie-like structure of size $m = |T|-\mathit{dup}(q,\mathcal{T})$, where $\mathit{dup}(q,\mathcal{T})$ is a quantity that represents the amount of redundancy that the SLP captures with respect to $q$-grams. The reduced problem can be solved in linear time. Since $m = O(qn)$, the running time of our algorithm is $O(\min\{|T|-\mathit{dup}(q,\mathcal{T}),qn\})$, improving our previous $O(qn)$ algorithm when $q = \Omega(|T|/n)$

Principles of Dataset Versioning: Exploring the Recreation/Storage Tradeoff

The relative ease of collaborative data science and analysis has led to a proliferation of many thousands or millions of $versions$ of the same datasets in many scientific and commercial domains, acquired or constructed at various stages of data analysis across many users, and often over long periods of time. Managing, storing, and recreating these dataset versions is a non-trivial task. The fundamental challenge here is the $storage-recreation\;trade-off$: the more storage we use, the faster it is to recreate or retrieve versions, while the less storage we use, the slower it is to recreate or retrieve versions. Despite the fundamental nature of this problem, there has been a surprisingly little amount of work on it. In this paper, we study this trade-off in a principled manner: we formulate six problems under various settings, trading off these quantities in various ways, demonstrate that most of the problems are intractable, and propose a suite of inexpensive heuristics drawing from techniques in delay-constrained scheduling, and spanning tree literature, to solve these problems. We have built a prototype version management system, that aims to serve as a foundation to our DATAHUB system for facilitating collaborative data science. We demonstrate, via extensive experiments, that our proposed heuristics provide efficient solutions in practical dataset versioning scenarios

The realization of input-output maps using bialgebras

The theory of bialgebras is used to prove a state space realization theorem for input/output maps of dynamical systems. This approach allows for the consideration of the classical results of Fliess and more recent results on realizations involving families of trees. Two examples of applications of the theorum are given

Elimination of Spurious Ambiguity in Transition-Based Dependency Parsing

We present a novel technique to remove spurious ambiguity from transition systems for dependency parsing. Our technique chooses a canonical sequence of transition operations (computation) for a given dependency tree. Our technique can be applied to a large class of bottom-up transition systems, including for instance Nivre (2004) and Attardi (2006)