A better upper bound on the number of triangulations of a planar point set

We show that a point set of cardinality $n$ in the plane cannot be the vertex set of more than $59^n O(n^{-6})$ straight-edge triangulations of its convex hull. This improves the previous upper bound of $276.75^n$.Comment: 6 pages, 1 figur

A Tractable Extension of Linear Indexed Grammars

It has been shown that Linear Indexed Grammars can be processed in polynomial time by exploiting constraints which make possible the extensive use of structure-sharing. This paper describes a formalism that is more powerful than Linear Indexed Grammar, but which can also be processed in polynomial time using similar techniques. The formalism, which we refer to as Partially Linear PATR manipulates feature structures rather than stacks.Comment: 8 pages LaTeX, uses eaclap.sty, to appear in EACL-9

Subtree power analysis finds optimal species for comparative genomics

Sequence comparison across multiple organisms aids in the detection of regions under selection. However, resource limitations require a prioritization of genomes to be sequenced. This prioritization should be grounded in two considerations: the lineal scope encompassing the biological phenomena of interest, and the optimal species within that scope for detecting functional elements. We introduce a statistical framework for optimal species subset selection, based on maximizing power to detect conserved sites. In a study of vertebrate species, we show that the optimal species subset is not in general the most evolutionarily diverged subset. Our results suggest that marsupials are prime sequencing candidates.Comment: 16 pages, 3 figures, 3 table

Setting Parameters by Example

We introduce a class of "inverse parametric optimization" problems, in which one is given both a parametric optimization problem and a desired optimal solution; the task is to determine parameter values that lead to the given solution. We describe algorithms for solving such problems for minimum spanning trees, shortest paths, and other "optimal subgraph" problems, and discuss applications in multicast routing, vehicle path planning, resource allocation, and board game programming.Comment: 13 pages, 3 figures. To be presented at 40th IEEE Symp. Foundations of Computer Science (FOCS '99

Low Ply Drawings of Trees

We consider the recently introduced model of \emph{low ply graph drawing}, in which the ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The \emph{ply-disk} of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest number of ply-disks having a common overlap is called the \emph{ply-number} of the drawing. We focus on trees. We first consider drawings of trees with constant ply-number, proving that they may require exponential area, even for stars, and that they may not even exist for bounded-degree trees. Then, we turn our attention to drawings with logarithmic ply-number and show that trees with maximum degree $6$ always admit such drawings in polynomial area.Comment: This is a complete access version of a paper that will appear in the proceedings of GD201

Fast Routing Table Construction Using Small Messages

We describe a distributed randomized algorithm computing approximate distances and routes that approximate shortest paths. Let n denote the number of nodes in the graph, and let HD denote the hop diameter of the graph, i.e., the diameter of the graph when all edges are considered to have unit weight. Given 0 < eps <= 1/2, our algorithm runs in weak-O(n^(1/2 + eps) + HD) communication rounds using messages of O(log n) bits and guarantees a stretch of O(eps^(-1) log eps^(-1)) with high probability. This is the first distributed algorithm approximating weighted shortest paths that uses small messages and runs in weak-o(n) time (in graphs where HD in weak-o(n)). The time complexity nearly matches the lower bounds of weak-Omega(sqrt(n) + HD) in the small-messages model that hold for stateless routing (where routing decisions do not depend on the traversed path) as well as approximation of the weigthed diameter. Our scheme replaces the original identifiers of the nodes by labels of size O(log eps^(-1) log n). We show that no algorithm that keeps the original identifiers and runs for weak-o(n) rounds can achieve a polylogarithmic approximation ratio. Variations of our techniques yield a number of fast distributed approximation algorithms solving related problems using small messages. Specifically, we present algorithms that run in weak-O(n^(1/2 + eps) + HD) rounds for a given 0 < eps <= 1/2, and solve, with high probability, the following problems: - O(eps^(-1))-approximation for the Generalized Steiner Forest (the running time in this case has an additive weak-O(t^(1 + 2eps)) term, where t is the number of terminals); - O(eps^(-2))-approximation of weighted distances, using node labels of size O(eps^(-1) log n) and weak-O(n^(eps)) bits of memory per node; - O(eps^(-1))-approximation of the weighted diameter; - O(eps^(-3))-approximate shortest paths using the labels 1,...,n.Comment: 40 pages, 2 figures, extended abstract submitted to STOC'1

An intelligent assistant for exploratory data analysis

In this paper we present an account of the main features of SNOUT, an intelligent assistant for exploratory data analysis (EDA) of social science survey data that incorporates a range of data mining techniques. EDA has much in common with existing data mining techniques: its main objective is to help an investigator reach an understanding of the important relationships ina data set rather than simply develop predictive models for selectd variables. Brief descriptions of a number of novel techniques developed for use in SNOUT are presented. These include heuristic variable level inference and classification, automatic category formation, the use of similarity trees to identify groups of related variables, interactive decision tree construction and model selection using a genetic algorithm

Compositional Explanation of Types and Algorithmic Debugging of Type Errors

The type systems of most typed functional programming languages are based on the Hindley-Milner type system. A practical problem with these type systems is that it is often hard to understand why a program is not type correct or a function does not have the intended type. We suggest that at the core of this problem is the difficulty of explaining why a given expression has a certain type. The type system is not defined compositionally. We propose to explain types using a variant of the Hindley-Milner type system that defines a compositional type explanation graph of principal typings. We describe how the programmer understands types by interactive navigation through the explanation graph. Furthermore, the explanation graph can be the foundation for algorithmic debugging of type errors, that is, semi-automatic localisation of the source of a type error without even having to understand the type inference steps. We implemented a prototype of a tool to explore the usefulness of the proposed methods