Paul Medvedev

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In the last several years, a number of studies have described large-scale structural variation in several genomes. Traditionally, such methods have used whole-genome array comparative genome hybridization or single-nucleotide polymorphism arrays to detect large regions subject to copy-number variation. Later techniques have been based on paired-end mapping(More)
MOTIVATION Genome assembly tools based on the de Bruijn graph framework rely on a parameter k, which represents a trade-off between several competing effects that are difficult to quantify. There is currently a lack of tools that would automatically estimate the best k to use and/or quickly generate histograms of k-mer abundances that would allow the user(More)
Graph-theoretic models have come to the forefront as some of the most powerful and practical methods for sequence assembly. Simultaneously, the computational hardness of the underlying graph algorithms has remained open. Here we present two theoretical results about the complexity of these models for sequence assembly. In the first part, we show sequence(More)
Distributed fair queueing in shared-medium ad hoc wireless networks is non-trivial because of the unique design challenges in such networks, such as location-dependent contention, distributed nature of ad hoc fair queueing, channel spatial reuse, and scalability in the presence of node mobility. In this paper, we seek to devise new distributed, localized,(More)
The development of high-throughput sequencing (HTS) technologies has opened the door to novel methods for detecting copy number variants (CNVs) in the human genome. While in the past CNVs have been detected based on array CGH data, recent studies have shown that depth-of-coverage information from HTS technologies can also be used for the reliable(More)
We study problems of reconfigurability of independent sets in graphs. We consider three different models (token jumping, token sliding, and token addition and removal) and analyze relationships between them. We prove that independent set reconfigurability in perfect graphs (under any of the three models) generalizes the shortest path reconfigurability(More)
Whole genome shotgun assembly is the process of taking many short sequenced segments (reads) and reconstructing the genome from which they originated. We demonstrate how the technique of bidirected network flow can be used to explicitly model the double-stranded nature of DNA for genome assembly. By combining an algorithm for the Chinese Postman Problem on(More)
MOTIVATION The continuing improvements to high-throughput sequencing (HTS) platforms have begun to unfold a myriad of new applications. As a result, error correction of sequencing reads remains an important problem. Though several tools do an excellent job of correcting datasets where the reads are sampled close to uniformly, the problem of correcting reads(More)
The mammalian Y Chromosome sequence, critical for studying male fertility and dispersal, is enriched in repeats and palindromes, and thus, is the most difficult component of the genome to assemble. Previously, expensive and labor-intensive BAC-based techniques were used to sequence the Y for a handful of mammalian species. Here, we present a much faster and(More)
We study the following problem on recon guring shortest paths in graphs: Given two shortest st paths, what is the minimum number of steps required to transform one into the other, where each intermediate path must also be a shortest s-t path and must di er from the previous one by only one vertex. We prove that the shortest recon guration sequence can be(More)