Showing papers by "Michael T. Goodrich published in 2020"

Reconstructing Binary Trees in Parallel

Abstract: We study the parallel query complexity of reconstructing binary trees from simple queries involving their nodes. We show that a querier can efficiently reconstruct a binary tree with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries.

Reconstructing Biological and Digital Phylogenetic Trees in Parallel

Abstract: In this paper, we study the parallel query complexity of reconstructing biological and digital phylogenetic trees from simple queries involving their nodes This is motivated from computational biology, data protection, and computer security settings, which can be abstracted in terms of two parties, a responder, Alice, who must correctly answer queries of a given type regarding a degree-d tree, T, and a querier, Bob, who issues batches of queries, with each query in a batch being independent of the others, so as to eventually infer the structure of T We show that a querier can efficiently reconstruct an n-node degree-d tree, T, with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries, including relative-distance queries and path queries Our results are all asymptotically optimal and improve the asymptotic (sequential) query complexity for one of the problems we study Moreover, through an experimental analysis using both real-world and synthetic data, we provide empirical evidence that our algorithms provide significant parallel speedups while also improving the total query complexities for the problems we study

Adaptive Exact Learning in a Mixed-Up World: Dealing with Periodicity, Errors and Jumbled-Index Queries in String Reconstruction

Abstract: We study the query complexity of exactly reconstructing a string from adaptive queries, such as substring, subsequence, and jumbled-index queries. Such problems have applications, e.g., in computational biology. We provide a number of new and improved bounds for exact string reconstruction for settings where either the string or the queries are “mixed-up”.

Adaptive Exact Learning in a Mixed-Up World: Dealing with Periodicity, Errors and Jumbled-Index Queries in String Reconstruction

Abstract: We study the query complexity of exactly reconstructing a string from adaptive queries, such as substring, subsequence, and jumbled-index queries. Such problems have applications, e.g., in computational biology. We provide a number of new and improved bounds for exact string reconstruction for settings where either the string or the queries are "mixed-up". For example, we show that a periodic (i.e., "mixed-up") string, $S=p^kp'$, of smallest period $p$, where $|p'|<|p|$, can be reconstructed using $O(\sigma|p|+\lg n)$ substring queries, where $\sigma$ is the alphabet size, if $n=|S|$ is unknown. We also show that we can reconstruct $S$ after having been corrupted by a small number of errors $d$, measured by Hamming distance. In this case, we give an algorithm that uses $O(d\sigma|p| + d|p|\lg \frac{n}{d+1})$ queries. In addition, we show that a periodic string can be reconstructed using $2\sigma\lceil\lg n\rceil + 2|p|\lceil\lg \sigma\rceil$ subsequence queries, and that general strings can be reconstructed using $2\sigma\lceil\lg n\rceil + n\lceil\lg \sigma\rceil$ subsequence queries, without knowledge of $n$ in advance. This latter result improves the previous best, decades-old result, by Skiena and Sundaram. Finally, we believe we are the first to study the exact-learning query complexity for string reconstruction using jumbled-index queries, which are a "mixed-up" typeA of query that have received much attention of late.

Reconstructing Biological and Digital Phylogenetic Trees in Parallel.

Abstract: In this paper, we study the parallel query complexity of reconstructing biological and digital phylogenetic trees from simple queries involving their nodes. This is motivated from computational biology, data protection, and computer security settings, which can be abstracted in terms of two parties, a responder, Alice, who must correctly answer queries of a given type regarding a degree-d tree, T, and a querier, Bob, who issues batches of queries, with each query in a batch being independent of the others, so as to eventually infer the structure of T. We show that a querier can efficiently reconstruct an n-node degree-d tree, T, with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries, including relative-distance queries and path queries. Our results are all asymptotically optimal and improve the asymptotic (sequential) query complexity for one of the problems we study. Moreover, through an experimental analysis using both real-world and synthetic data, we provide empirical evidence that our algorithms provide significant parallel speedups while also improving the total query complexities for the problems we study.

Inverse-rendering-based analysis of the fine illumination effects in Salvator Mundi

Abstract: The painting Salvator Mundi is attributed to Leonardo da Vinci and depicts Jesus holding a transparent orb. The authors study the optical accuracy of the fine illumination effects in this painting using inverse rendering. Their experimental results provide plausible explanations for the strange glow inside the orb, the anomalies on the orb and the mysterious three white spots, supporting the optical accuracy of the orb's rendering down to its fine-grain details.