We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

BIOE 402. Medical Technology Assessment. 2 or 3 hours. Bioentrepreneur course. Assessment of medical technology in the context of commercialization. Objectives, competition, market share, funding, pricing, manufacturing, growth, and intellectual property; many issues unique to biomedical products. Course Information: 2 undergraduate hours. 3 graduate hours. Prerequisite(s): Junior standing or above and consent of the instructor.

“Bioinformatics” 특집을 내면서

Here, we present a major advance of the OrthoFinder method. This extends OrthoFinder’s high accuracy orthogroup inference to provide phylogenetic inference of orthologs, rooted gene trees, gene duplication events, the rooted species tree, and comparative genomics statistics. Each output is benchmarked on appropriate real or simulated datasets, and where comparable methods exist, OrthoFinder is equivalent to or outperforms these methods. Furthermore, OrthoFinder is the most accurate ortholog inference method on the Quest for Orthologs benchmark test. Finally, OrthoFinder’s comprehensive phylogenetic analysis is achieved with equivalent speed and scalability to the fastest, score-based heuristic methods. OrthoFinder is available at https://github.com/davidemms/OrthoFinder.

/pdf/orthofinder-phylogenetic-orthology-inference-for-comparative-3igntoeigs.pdf

OrthoFinder: phylogenetic orthology inference for comparative genomics

https://www.cse.unsw.edu.au/~cs9314/07s1/lectures/Lin_CS9314_References/cm-latin.pdf

An improved data stream summary: the count-min sketch and its applications

In the data stream scenario, input arrives very rapidly and there is limited memory to store the input. Algorithms have to work with one or few passes over the data, space less than linear in the input size or time significantly less than the input size. In the past few years, a new theory has emerged for reasoning about algorithms that work within these constraints on space, time, and number of passes. Some of the methods rely on metric embeddings, pseudo-random computations, sparse approximation theory and communication complexity. The applications for this scenario include IP network traffic analysis, mining text message streams and processing massive data sets in general. Researchers in Theoretical Computer Science, Databases, IP Networking and Computer Systems are working on the data stream challenges. This article is an overview and survey of data stream algorithmics and is an updated version of [1].

/pdf/data-streams-algorithms-and-applications-5fo85u5tcy.pdf

Data streams: algorithms and applications

We present a 1-pass algorithm for estimating the most frequent items in a data stream using limited storage space. Our method relies on a data structure called a COUNT SKETCH, which allows us to reliably estimate the frequencies of frequent items in the stream. Our algorithm achieves better space bounds than the previously known best algorithms for this problem for several natural distributions on the item frequencies. In addition, our algorithm leads directly to a 2-pass algorithm for the problem of estimating the items with the largest (absolute) change in frequency between two data streams. To our knowledge, this latter problem has not been previously studied in the literature.

/pdf/finding-frequent-items-in-data-streams-1kwsh6co7z.pdf

Finding Frequent Items in Data Streams

We present a very simple algorithm for the Least Common Ancestors problem. We thus dispel the frequently held notion that optimal LCA computation is unwieldy and unimplementable. Interestingly, this algorithm is a sequentialization of a previously known PRAM algorithm.

/pdf/the-lca-problem-revisited-1u8rpa0sa7.pdf

The LCA Problem Revisited

Large scale gene duplication is a major force driving the evolution of genetic functional innovation. Whole genome duplications are widely believed to have played an important role in the evolution of the maize, yeast, and vertebrate genomes. The use of evolutionary trees to analyze the history of gene duplication and estimate duplication times provides a powerful tool for studying this process. Many studies in the molecular evolution literature have used this approach on small data sets, using analyses performed by hand. The rapid growth of genetic sequence data will soon allow similar studies on a genomic scale, but such studies will be limited unless the analysis can be automated. Even existing data sets admit alternative hypotheses that would be too tedious to consider without automation. In this paper, we describe a program called NOTUNG that facilitates large scale analysis, using both rooted and unrooted trees. When tested on trees analyzed in the literature, NOTUNG consistently yielded results that agree with the assessments in the original publications. Thus, NOTUNG provides a basic building block for inferring duplication dates from gene trees automatically and can also be used as an exploratory analysis tool for evaluating alternative hypotheses.

/pdf/notung-a-program-for-dating-gene-duplications-and-optimizing-nbllw0z6tq.pdf

NOTUNG: a program for dating gene duplications and optimizing gene family trees.

The suffix tree of a string is the fundamental data structure of combinatorial pattern matching. We present a recursive technique for building suffix trees that yields optimal algorithms in different computational models. Sorting is an inherent bottleneck in building suffix trees and our algorithms match the sorting lower bound. Specifically, we present the following results. (1) Weiner [1973], who introduced the data structure, gave an optimal 0(n)-time algorithm for building the suffix tree of an n-character string drawn from a constant-size alphabet. In the comparison model, there is a trivial O(n log n)-time lower bound based on sorting, and Weiner's algorithm matches this bound. For integer alphabets, the fastest known algorithm is the O(n log n)time comparison-based algorithm, but no super-linear lower bound is known. Closing this gap is the main open question in stringology. We settle this open problem by giving a linear time reduction to sorting for building suffix trees. Since sorting is a lower-bound for building suffix trees, this algorithm is time-optimal in every alphabet mode. In particular, for an alphabet consisting of integers in a polynomial range we get the first known linear-time algorithm. (2) All previously known algorithms for building suffix trees exhibit a marked absence of locality of reference, and thus they tend to elicit many page faults (I/Os) when indexing very long strings. They are therefore unsuitable for building suffix trees in secondary storage devices, where I/Os dominate the overall computational cost. We give a linear-I/O reduction to sorting for suffix tree construction. Since sorting is a trivial I/O-lower bound for building suffix trees, our algorithm is I/O-optimal.

Martin Farach-Colton

Papers

Finding Frequent Items in Data Streams

The LCA Problem Revisited

NOTUNG: a program for dating gene duplications and optimizing gene family trees.

On the sorting-complexity of suffix tree construction

Lowest common ancestors in trees and directed acyclic graphs