Michael Piatek

Profiling a million user dht

Distributed hash tables (DHTs) provide scalable, key-based lookup of objects in dynamic network environments. Although DHTs have been studied extensively from an analytical perspective, only recently have wide deployments enabled empirical examination. This paper reports measurements of the Azureus BitTorrent clients DHT, which is in active use by more than 1 million nodes on a daily basis. The Azureus DHT operates on untrusted, unreliable end-hosts, offering a glimpse into the implementation challenges associated with making structured overlays work in practice. Our measurements provide characterizations of churn, overhead, and performance in this environment. We leverage these measurements to drive the design of a modified DHT lookup algorithm that reduces median DHT lookup time by an order of magnitude for a nominal increase in overhead.

Leveraging bittorrent for end host measurements

Traditional methods of conducting measurements to end hosts require sending unexpected packets to measurement targets. Although existing techniques can ascertain end host characteristics accurately, their use in large-scale measurement studies is hindered by the fact that unexpected traffic can trigger alarms in common intrusion detection systems, often resulting in complaints from administrators. We describe BitProbes, a measurement system that works around this challenge. By coordinated participation in the popular peer-to-peer BitTorrent system, BitProbes is able to unobtrusively measure bandwidth capacity, latency, and topology information for ∼500,000 end hosts per week from only eight vantage points at the University of Washington. To date, our measurements have not generated a single complaint in spite of their wide coverage.

Knot Tightening by Constrained Gradient Descent

We present new computations of approximately length-minimizing polygons with fixed thickness. These curves model the centerlines of “tight” knotted tubes with minimal length and fixed circular cross-section. Our curves approximately minimize the ropelength (or quotient of length and thickness) for polygons in their knot types. While previous authors have minimized ropelength for polygons using simulated annealing, the new idea in our code is to minimize length over the set of polygons of thickness at least one using a version of constrained gradient descent. We rewrite the problem in terms of minimizing the length of the polygon subject to an infinite family of differentiable constraint functions. We prove that the set of variations of a polygon of thickness one that does not decrease thickness to first order is a finitely generated polyhedral cone, and give an explicit set of generators. Using this cone, we give a first-order minimization procedure and a Karush–Kuhn–Tucker criterion for polygonal-ropelength criticality. Our main numerical contribution is a set of 379 almost-critical knots and links, including all prime knots with ten and fewer crossings and all prime links with nine and fewer crossings. For links, these are the first published ropelength figures, and for knots they improve on existing figures. We give new maps of the self-contacts of these knots and links, and discover some highly symmetric tight knots with particularly simple-looking self-contact maps.

Thialfi: a client notification service for internet-scale applications

Ensuring the freshness of client data is a fundamental problem for applications that rely on cloud infrastructure to store data and mediate sharing. Thialfi is a notification service developed at Google to simplify this task. Thialfi supports applications written in multiple programming languages and running on multiple platforms, e.g., browsers, phones, and desktops. Applications register their interest in a set of shared objects and receive notifications when those objects change. Thialfi servers run in multiple Google data centers for availability and replicate their state asynchronously. Thialfis approach to recovery emphasizes simplicity: all server state is soft, and clients drive recovery and assist in replication. A principal goal of our design is to provide a straightforward API and good semantics despite a variety of failures, including server crashes, communication failures, storage unavailability, and data center failures. Evaluation of live deployments confirms that Thialfi is scalable, efficient, and robust. In production use, Thialfi has scaled to millions of users and delivers notifications with an average delay of less than one second.

Visualizing the tightening of knots

The study of physical models for knots has recently received much interest in the mathematics community. In this paper, we consider the ropelength model, which considers knots tied in an idealized rope. This model is interesting in pure mathematics, and has been applied to the study of a variety of problems in the natural sciences as well. Modeling and visualizing the tightening of knots in this idealized rope poses some interesting challenges in computer graphics. In particular, self-contact in a deformable rope model is a difficult problem which cannot be handled by standard techniques. In this paper, we describe a solution based on reformulating the contact problem and using constrained-gradient techniques from nonlinear optimization. The resulting animations reveal new properties of the tightening flow and provide new insights into the geometric structure of tight knots and links.

Effect of knotting on polymer shapes and their enveloping ellipsoids

We simulate freely jointed chains to investigate how knotting affects the overall shapes of freely fluctuating circular polymeric chains. To characterize the shapes of knotted polygons, we construct enveloping ellipsoids that minimize volume while containing the entire polygon. The lengths of the three principal axes of the enveloping ellipsoids are used to define universal size and shape descriptors analogous to the squared radius of gyration and the inertial asphericity and prolateness. We observe that polymeric chains forming more complex knots are more spherical and also more prolate than chains forming less complex knots with the same number of edges. We compare the shape measures, determined by the enveloping ellipsoids, with those based on constructing inertial ellipsoids and explain the differences between these two measures of polymer shape.

POLYGONAL KNOT SPACE NEAR ROPELENGTH-MINIMIZED KNOTS

For a polygonal knot K, it is shown that a tube of radius R(K), the polygonal thickness radius, is an embedded torus. Given a thick configuration K, perturbations of size r < R(K) define satellite structures, or local knotting. We explore knotting within these tubes both theoretically and numerically. We provide bounds on perturbation radii for which one can obtain small trefoil and figure-eight summands and use Monte Carlo simulations to estimate the relative probabilities of these structures as a function of the number of edges.