Mash extends the MinHash dimensionality-reduction technique to include a pairwise mutation distance and P value significance test, enabling the efficient clustering and search of massive sequence collections. Mash reduces large sequences and sequence sets to small, representative sketches, from which global mutation distances can be rapidly estimated. We demonstrate several use cases, including the clustering of all 54,118 NCBI RefSeq genomes in 33 CPU h; real-time database search using assembled or unassembled Illumina, Pacific Biosciences, and Oxford Nanopore data; and the scalable clustering of hundreds of metagenomic samples by composition. Mash is freely released under a BSD license (
 https://github.com/marbl/mash
 ).

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Mash: fast genome and metagenome distance estimation using MinHash.

In this article, we give an overview of efficient algorithms for the approximate and exact nearest neighbor problem. The goal is to preprocess a dataset of objects (e.g., images) so that later, given a new query object, one can quickly return the dataset object that is most similar to the query. The problem is of significant interest in a wide variety of areas.

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Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions

This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.

Parameterized Algorithms

We present an algorithm for the c-approximate nearest neighbor problem in a d-dimensional Euclidean space, achieving query time of O\left( {dn^{1/c^2 + o(1)} } \right) and space O\left( {dn + n^{1 + 1/c^2 + o(1)} } \right). This almost matches the lower bound for hashing-based algorithm recently obtained in [27]. We also obtain a space-efficient version of the algorithm, which uses dn+n log^{O(1)} n space, with a query time of dn^{O(1/c^2 )}. Finally, we discuss practical variants of the algorithms that utilize fast bounded-distance decoders for the Leech Lattice.

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Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions

We present two algorithms for the approximate nearest neighbor problem in high dimensional spaces. For data sets of size n living in IR, the algorithms require space that is only polynomial in n and d, while achieving query times that are sub-linear in n and polynomial in d. We also show applications to other high-dimensional geometric problems, such as the approximate minimum spanning tree.

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Approximate Nearest Neighbor: Towards Removing the Curse of Dimensionality

We present several new results on one of the most extensively studied topics in computational geometry, orthogonal range searching. All our results are in the standard word RAM model for points in rank space: 
** We present two data structures for 2-d orthogonal range emptiness. The first achieves O(n lglg n) space and O(lglg n) query time. This improves the previous results by Alstrup, Brodal, and Rauhe(FOCS'00), with O(n lg^eps n) space and O(lglg n) query time, or with O(nlglg n) space and O(lg^2 lg n) query time. Our second data structure uses O(n) space and answers queries in O(lg^eps n) time. The best previous O(n)-space data structure, due to Nekrich (WADS'07), answers queries in O(lg n/lglg n) time. 
** For 3-d orthogonal range reporting, we obtain space O(n lg^{1+eps} n) and query time O(lglg n + k), for any constant eps>0. This improves previous results by Afshani (ESA'08), Karpinski and Nekrich (COCOON'09), and Chan (SODA'11), with O(n lg^3 n) space and O(lglg n + k) query time, or with O(n lg^{1+eps} n) space and O(lg^2 lg n + k) query time. This implies improved bounds for orthogonal range reporting in all constant dimensions above 3. 
** We give a randomized algorithm for 4-d offline dominance range reporting/emptiness with running time O(n lg n + k). This resolves two open problems from Preparata and Shamos' seminal book: 
**** given n axis-aligned rectangles in the plane, we can report all k enclosure pairs in O(n lg n + k) expected time. The best known result was an O([n lg n + k] lglg n) algorithm from SoCG'95 by Gupta, Janardan, Smid, and Dasgupta. 
**** given n points in 4-d, we can find all maximal points in O(n lg n) expected time. The best previous result was an O(n lg n lglg n) algorithm due to Gabow, Bentley, and Tarjan (STOC'84). This implies record time bounds for the maxima problem in all constant dimensions above 4.

Orthogonal Range Searching on the RAM, Revisited

In this paper, the accent is on modeling the stick–slip phenomenon of micro devices, where a case shall be presented from the field of scanning probe microactuators. The case is about the μWalker, an electrostatic stepper motor which can deliver forces up to 1.7 mN and has ranges up to 140 μm. For the sake of a reliable operation, it is very important to control the stick–slip effects at the sliding surfaces. In order to introduce the stick–slip effect, a basic model of a mass, spring and sliding surface is presented, accompanied by simulation results. The total model of the device is then shown, again stressing the stick–slip phenomenon at the two sliding surfaces. Simulations from the model presented fit the measurements and can also predict step sizes as a function of varying inputs. Using a model for predictions is very attractive when looking for a way to decrease development cost and time.

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Modeling and simulating the stick–slip motion of the μWalker, a MEMS-based device for μSPAM

We show how to hang a picture by wrapping rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when fewer than k nails get removed. This construction makes for some fun mathematical magic performances. More generally, we characterize the possible Boolean functions characterizing when the picture falls in terms of which nails get removed as all monotone Boolean functions. This construction requires an exponential number of twists in the worst case, but exponential complexity is almost always necessary for general functions.

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Picture-Hanging Puzzles

This paper is about the /spl mu/Walker, an electrostatic stepper motor mainly intended for positioning the data probes with respect to the storage medium in a data storage device. It can deliver forces up to 1.7 mN for ranges as large as 140 /spl mu/m. Controlling the stick-slip effects at the sliding surfaces is of central importance for reliable operation. A model is introduced to estimate the operating voltage of the actuator plate, which is an essential part of the /spl mu/Walker. Several methods to obtain displacements smaller than one nominal step (/spl ap/ 50 nm) are discussed, as well as how to increase the step repeatability and accuracy.

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Mihai Patrascu

Papers

Orthogonal Range Searching on the RAM, Revisited

Modeling and simulating the stick–slip motion of the μWalker, a MEMS-based device for μSPAM

Picture-Hanging Puzzles

Stick-slip actuation of electrostatic stepper micropositioners for data storage-the /spl mu/walker

Corrigendum to "efficient similarity search and classification via rank aggregation" by Ronald Fagin, Ravi Kumar and D. Sivakumar (proc. SIGMOD'03)