ICS Theory Seminar

More Robust Hashing: Cuckoo Hashing with a Stash

Fri, 21 Nov 2008 19:00:00 GMT

November 21, Fall 2008: Theory Seminar

More Robust Hashing: Cuckoo Hashing with a Stash

by Adam Kirsch, Michael Mitzenmacher, and Udi Wieder

Appeared at European Symposium on Algorithms (ESA) 2008

Presented by Kevin Wortman

Cuckoo hashing holds great potential as a high-performance hashing scheme for real applications. Up to this point, the greatest drawback of cuckoo hashing appears to be that there is a polynomially small but practically significant probability that a failure occurs during the insertion of an item, requiring an expensive rehashing of all items in the table. In this paper, we show that this failure probability can be dramatically reduced by the addition of a very small constant-sized stash. We demonstrate both analytically and through simulations that stashes of size equivalent to only three or four items yield tremendous improvements, enhancing cuckoo hashing's practical viability in both hardware and software. Our analysis naturally extends previous analyses of multiple cuckoo hashing variants, and the approach may prove useful in further related schemes.

Some Results on Greedy Embeddings in Metric Spaces (FOCS 2008)

Fri, 14 Nov 2008 19:00:00 GMT

November 14, Fall 2008: Theory Seminar

Some Results on Greedy Embeddings in Metric Spaces (FOCS 2008)

By Tom Leighton and Ankur Moitra

Presented by Darren Strash

I will discuss a recent proof that resolves a conjecture of Papadimitriou and Ratajczak---that every 3-connected planar graph admits a greedy embedding into the Euclidean plane.

Embedding Planar Graphs on the Grid

Fri, 07 Nov 2008 19:00:00 GMT

November 7, Fall 2008: Theory Seminar

Embedding Planar Graphs on the Grid

By Walter Schnyder

Presented by Lowell Trott

We will discuss the method that Schnyder uses to embed graphs, as well as some interesting results gained from his method.

Firefighting in Trees and Infinite Grids.

Fri, 31 Oct 2008 19:00:00 GMT

October 31, Fall 2008: Theory Seminar

1:00pm in 253 ICS

Firefighting in Trees and Infinite Grids.

Nate Gertsch

I'll be explaining the firefighter problem and show that the problem has some interesting results in infinite grids of various dimensions and on trees.

Two results on 3d lattice embedding of graphs

Fri, 24 Oct 2008 19:00:00 GMT

October 24, Fall 2008: Theory Seminar

1:00pm in 253 ICS

Two results on 3d lattice embedding of graphs

Prof. David Eppstein, UC Irvine

I'll present the results from two of my papers at Graph Drawing 2008: "Isometric diamond subgraphs", about embedding graphs into the three-dimensional diamond lattice, and "The topology of three-dimensional bendless orthogonal graph drawing", about embedding graphs into space in such a way that three mutually orthogonal edges meet at each vertex.

Succinct Greedy Graph Drawing in the Hyperbolic Plane

Fri, 17 Oct 2008 19:00:00 GMT

October 17, Fall 2008: Theory Seminar

1:00pm in 253 ICS

Succinct Greedy Graph Drawing in the Hyperbolic Plane

Prof. Michael Goodrich, UC Irvine

Abstract: We describe an efficient method for drawing any n-vertex simple graph G in the hyperbolic plane. Our algorithm produces greedy drawings, which support greedy geometric routing, so that a message M between any pair of vertices may be routed geometrically, simply by having each vertex that receives M pass it along to any neighbor that is closer in the hyperbolic metric to the message's eventual destination. More importantly, for networking applications, our algorithm produces succinct drawings, in that each of the vertex positions in one of our embeddings can be represented using O(log n) bits and the calculation of which neighbor to send a message to may be performed efficiently using these representations. These properties are useful, for example, for routing in sensor networks, where storage and bandwidth are limited.

Joint work with David Eppstein.

> Self-Improving Algorithms for Delaunay Triangulations

Fri, 10 Oct 2008 19:00:00 GMT

October 10, Fall 2008: Theory Seminar

1:00pm in 253 ICS

> Self-Improving Algorithms for Delaunay Triangulations

Ken Clarkson, IBM Almaden Research Center

This work investigates ways in which an algorithm can improve its expected performance by fine-tuning itself automatically, with respect to an arbitrary and unknown input distribution. We give such self-improving algorithms for sorting and for computing Delaunay triangulations. Each algorithm begins with a training phase during which it adjusts itself to the input distribution, followed by a stationary regime in which the algorithm settles to its optimized incarnation. We show that in both cases, in the stationary regime, the algorithms run as fast as possible.

Joint work with Nir Alon, Bernard Chazelle, Ding Liu, C. Seshadhri, and Wolfgang Mulzer.

Improved bounds for Wireless Localization

Fri, 03 Oct 2008 19:00:00 GMT

October 3, Fall 2008: Theory Seminar

1:00pm in ICS 253

Improved bounds for Wireless Localization

By Tobias Christ, Michael Hoffmann, Yoshio Okamoto and Takeaki Uno, appeared in SWAT 2008.

Presented by Nodari Sitchinava

I will talk about the recent paper showing better upper and lower bounds for wireless localization. In particular, for an n-sided polygon, n-2 guards is the tight bound if we require guards to be natural. For arbitrary guards, the new lower and upper bounds are, respectively, roughly 3n/5 and 4n/5. I'll present the proofs of these bounds.

A Randomized Algorithm for Constructing the Trapezoidal Map Induced by a Connected Geometric Graph

Fri, 06 Jun 2008 19:00:00 GMT

CompSci 269S, Winter 2008: Theory Seminar

June 6, 2008, 1:00pm in Bren Hall 1423

A Randomized Algorithm for Constructing the Trapezoidal Map Induced by a Connected Geometric Graph

Darren Strash

Abstract:

We discuss the general problem of constructing the trapezoidal map induced by a set of line segments in the plane, and present preliminary results for a randomized algorithm for the special case when the line segments form a connected geometric graph.

This is joint work with Michael Goodrich.

Offline Variants of the "Lion and Man" Problem

Fri, 09 May 2008 19:00:00 GMT

CompSci 269S, Winter 2008: Theory Seminar

May 9, 2008, 1:00pm in Bren Hall 1423

Offline Variants of the "Lion and Man" Problem

authored by Adrian Dumitrescu, Ichiro Suzuki, and Pawel Zylinski

Appeared at SOCG 2007 http://portal.acm.org/citation.cfm?id=1247069.1247085&coll=GUIDE&dl=GUIDE

presented by Kevin Wortman

Abstract:

Consider the following survival problem:Given a set of k trajectories (paths) with maximum unit speed in a bounded region over a (long) time interval [0,T], find another trajectory (if it exists) subject to the same maximum unit speed limit, that avoids (that is, stays at a safe distance of) each of the other trajectories over the entire time interval. We call this variant the continuous model of the survival problem. The discrete model of this problem is: Given the trajectories (paths) of k point robots in a graph over a (long) time interval 0,1,2,...,T, find a trajectory (path) for another robot, that avoids each of the other k at any time instance in thegiven time interval. We introduce the notions of survival number of a region,and that of a graph, respectively, as the maximum number of trajectories which can be avoided in the region (resp. graph). We give the first estimates on the survival number of the n x n grid Gn, and also devise an efficient algorithm for the corresponding safe path planning problem in arbitrary graphs. We then show that our estimates on the survival number of Gn on the number of paths that can be avoided in Gn can be extended for the survival number of a bounded (square) region. In the final part of our paper, we consider other related offline questions, such as the maximum number of men problem and the spy problem.

Finding Optimal Refueling Policies in Transportation Networks

Fri, 25 Apr 2008 19:00:00 GMT

CompSci 269S, Winter 2008: Theory Seminar

Apr 25, 2008, 1:00pm in Bren Hall 1423

Finding Optimal Refueling Policies in Transportation Networks

authored by Shieu-Hong Lin

presented by Nate Gertsch

Abstract:

We study the combinational properties of optimal refueling policies, which specify the transportation paths and refueling operations along the paths to minimize the total transportation costs between vertices.

Graph Algorithms in PEM: Part II

Fri, 18 Apr 2008 19:00:00 GMT

CompSci 269S, Winter 2008: Theory Seminar

Apr 18, 2008, 1:00pm in Bren Hall 1423

Graph Algorithms in PEM: Part II

presented by Nodari Sitchinava

Abstract:

This is the second part in the two part series on graph algorithms in the Parallel External Memory model. I will present algorithms for finding connected and bi-connected components, minimum spanning trees and ear decomposition in graphs; tree contraction, expression tree evaluation and lowest common ancestor queries on trees. All these solutions use Euler tour technique as the building block just like in the PRAM algorithms. Therefore, I'll review this technique and simple problems one can solve with it in parallel.

This is joint work with Lars Arge and Michael Goodrich.

Parallel External Memory Graph Algorithms

Fri, 14 Mar 2008 19:00:00 GMT

CompSci 269S, Winter 2008: Theory Seminar

Mar 14, 2008, 1:00pm in Bren Hall 1423

Parallel External Memory Graph Algorithms

Nodari Sitchinava

Abstract:

I will be presenting new results in Parallel External Memory model. In particular I will talk about solutions to List ranking, Euler tour technique and its application to problems on trees, finding connected components and the minimum spanning tree of an undirected graph.

This is joint work with Lars Arge and Mike Goodrich.

Fast Algorithms for Minimum Weight Constant Length Cycles in Edge-Weighted Graphs

Fri, 07 Mar 2008 19:00:00 GMT

CompSci 269S, Winter 2008: Theory Seminar

Mar 7, 2008, 1:00pm in Bren Hall 1423

Fast Algorithms for Minimum Weight Constant Length Cycles in Edge-Weighted Graphs

presented by Mike Nelson

Abstract:

I will present some results from "Finding the Smallest H-Subgraph in Real Weighted Graphs and Related Problems", by Virginia Vassilevska, Ryan Williams, and Raphael Yuster. This work appeared in the International Colloquium on Autotmata, Languages and Programming 2006. I will present their deterministic algorithm for finding the minimum weight cycle of length k. For a fixed (constant) k, the algorithm has running time that is sub-quadratic in m, the number of edges.

The Graph Genus Problem is NP-Complete

Fri, 29 Feb 2008 19:00:00 GMT

CompSci 269S, Winter 2008: Theory Seminar

Feb 29, 2008, 1:00pm in Bren Hall 1423

The Graph Genus Problem is NP-Complete

by Carsten Thomassen, in Journal of Algorithms 10:4 (1989)

presented by Darren Strash

Abstract:

It is NP-complete to tell, given a graph /G/ and a natural number /k/, whether /G/ has genus /k/ or less.

On the Complexity of Delaunay Triangulations on Manifolds

Fri, 22 Feb 2008 19:00:00 GMT

CompSci 269S, Winter 2008: Theory Seminar

Feb 22, 2008, 1:00pm in Bren Hall 1423

On the Complexity of Delaunay Triangulations on Manifolds

Nina Amenta (UC Davis)

Abstract:

Even more than most spatial data structures, the Delaunay triangulation suffers from the "curse of dimensionality". A classic theorem of McMullen says that the worst-case complexity of the Delaunay triangulation of a set of n points in dimension d is θ(n^⌈d/2⌉). The point sets constructed to realize this exponential bound are distributed on one-dimensional curves. What about distributions of points on manifolds of dimension 1 < p ≤ d?

We consider sets of points distributed nearly uniformly on a polyhedral surfaces of dimension p, and find that their Delaunay triangulations have complexity O(n^(d-k+1)/p), with k being the ceiling of (d+1)/(p+1), and we show that this bound is tight.

Nondecreasing Paths in a Weighted Graph or: How to Optimally Read a Train Schedule

Fri, 15 Feb 2008 19:00:00 GMT

CompSci 269S, Winter 2008: Theory Seminar

Feb 15, 2008, in Bren Hall 1423

Nondecreasing Paths in a Weighted Graph or: How to Optimally Read a Train Schedule

by Virginia Vassilevska, appeared at SODA 2008

presented by Kevin Wortman

Abstract:

A travel booking office has timetables giving arrival and departure times for all scheduled trains, including their origins and destinations. A customer presents a starting city and demands a route with perhaps several train connections taking him to his destination as early as possible. The booking office must find the best route for its customers. This problem was first considered in the theory of algorithms by George Minty, who reduced it to a problem on directed weighted graphs: find a path from a given source to a given target such that the consecutive weights on the path are nondecreasing and the last weight on the path is minimized. Minty gave the first algorithm for the single source version of the problem, in which one finds minimum last weight nondecreasing paths from the source to every other vertex. In this paper we give the first linear time algorithm for this problem. We also define an all pairs version for the problem and give a strongly polynomial truly subcubic algorithm for it.

Balloon Popping With Applications to Ascending Auctions

Fri, 30 Nov 2007 19:00:00 GMT

CompSci 269S, Fall 2007: Theory Seminar

November 30, 2007, 1:00pm, in Bren Hall 1423

Balloon Popping With Applications to Ascending Auctions

(from FOCS 2007) authored by Nicole Immorlica, Anna R Karlin, Mohammad Mahdian, and Kunal Talwar

presented by Matt Nguyen

Abstract:

The authors study the power of ascending auctions in a scenario in which a seller is selling a collection of identical items to anonymous unit-demand bidders. They show that even with full knowledge of the set of bidders' private valuations for the items, if the bidders are ex-ante identical, no ascending auction can extract more than a constant times the revenue of the best fixed price scheme.

This problem is equivalent to the problem of coming up with an optimal strategy for blowing up indistinguishable balloons with known capacities in order to maximize the amount of contained air. They show that the algorithm which simply inflates all balloons to a fixed volume is close to optimal in this setting.

Computing Similarity in Collaborate Filtering Systems

Fri, 16 Nov 2007 19:00:00 GMT

CompSci 269S, Fall 2007: Theory Seminar

November 16, 2007, 1:00pm, in Bren Hall 1423

Computing Similarity in Collaborate Filtering Systems

presented by Nate Gertsch

Abstract:

not yet available

Distribution Sort in PEM Model

Fri, 09 Nov 2007 19:00:00 GMT

CompSci 269S, Fall 2007: Theory Seminar

November 9, 2007, 1:00pm, in Bren Hall 1423

Distribution Sort in PEM Model

presented by Nodari Sitchinava

Abstract:

This talk will present preliminary results on selection and distribution sort in the Parallel External Memory (PEM) Model.

This is joint work with Lars Arge and Michael Goodrich.