[Review of] Christie Davies. Ethnic Humor Around the World: A Comparative Analysis

If you want to know what\u27s in Davies\u27 Ethnic Humor Around the World, you\u27ll need to devote some time and energy to the matter. It\u27s a serious study-not the kind you can read at the bus stop or listen to in bits and pieces on a cassette or read excerpted in a popular magazine. Nevertheless, this is a must-read for anyone who\u27s tempted to make such blanket statements as the one that climaxes a currently popular video tape on cultural diversity: There is no place in business or academics for ethnic joking

Faster Deterministic Fully-Dynamic Graph Connectivity

We give new deterministic bounds for fully-dynamic graph connectivity. Our data structure supports updates (edge insertions/deletions) in $O(\log^2n/\log\log n)$ amortized time and connectivity queries in $O(\log n/\log\log n)$ worst-case time, where $n$ is the number of vertices of the graph. This improves the deterministic data structures of Holm, de Lichtenberg, and Thorup (STOC 1998, J.ACM 2001) and Thorup (STOC 2000) which both have $O(\log^2n)$ amortized update time and $O(\log n/\log\log n)$ worst-case query time. Our model of computation is the same as that of Thorup, i.e., a pointer machine with standard $AC^0$ instructions.Comment: To appear at SODA 2013. 19 pages, 1 figur

Approximate Distance Oracles for Planar Graphs with Improved Query Time-Space Tradeoff

We consider approximate distance oracles for edge-weighted n-vertex undirected planar graphs. Given fixed epsilon > 0, we present a (1+epsilon)-approximate distance oracle with O(n(loglog n)^2) space and O((loglog n)^3) query time. This improves the previous best product of query time and space of the oracles of Thorup (FOCS 2001, J. ACM 2004) and Klein (SODA 2002) from O(n log n) to O(n(loglog n)^5).Comment: 20 pages, 9 figures of which 2 illustrate pseudo-code. This is the SODA 2016 version but with the definition of C_i in Phase I fixed and the analysis slightly modified accordingly. The main change is in the subsection bounding query time and stretch for Phase

Minimum Cycle Basis and All-Pairs Min Cut of a Planar Graph in Subquadratic Time

A minimum cycle basis of a weighted undirected graph $G$ is a basis of the cycle space of $G$ such that the total weight of the cycles in this basis is minimized. If $G$ is a planar graph with non-negative edge weights, such a basis can be found in $O(n^2)$ time and space, where $n$ is the size of $G$. We show that this is optimal if an explicit representation of the basis is required. We then present an $O(n^{3/2}\log n)$ time and $O(n^{3/2})$ space algorithm that computes a minimum cycle basis \emph{implicitly}. From this result, we obtain an output-sensitive algorithm that explicitly computes a minimum cycle basis in $O(n^{3/2}\log n + C)$ time and $O(n^{3/2} + C)$ space, where $C$ is the total size (number of edges and vertices) of the cycles in the basis. These bounds reduce to $O(n^{3/2}\log n)$ and $O(n^{3/2})$, respectively, when $G$ is unweighted. We get similar results for the all-pairs min cut problem since it is dual equivalent to the minimum cycle basis problem for planar graphs. We also obtain $O(n^{3/2}\log n)$ time and $O(n^{3/2})$ space algorithms for finding, respectively, the weight vector and a Gomory-Hu tree of $G$. The previous best time and space bound for these two problems was quadratic. From our Gomory-Hu tree algorithm, we obtain the following result: with $O(n^{3/2}\log n)$ time and $O(n^{3/2})$ space for preprocessing, the weight of a min cut between any two given vertices of $G$ can be reported in constant time. Previously, such an oracle required quadratic time and space for preprocessing. The oracle can also be extended to report the actual cut in time proportional to its size

Objective acceleration for unconstrained optimization

Acceleration schemes can dramatically improve existing optimization procedures. In most of the work on these schemes, such as nonlinear Generalized Minimal Residual (N-GMRES), acceleration is based on minimizing the $\ell_2$ norm of some target on subspaces of $\mathbb{R}^n$. There are many numerical examples that show how accelerating general purpose and domain-specific optimizers with N-GMRES results in large improvements. We propose a natural modification to N-GMRES, which significantly improves the performance in a testing environment originally used to advocate N-GMRES. Our proposed approach, which we refer to as O-ACCEL (Objective Acceleration), is novel in that it minimizes an approximation to the \emph{objective function} on subspaces of $\mathbb{R}^n$. We prove that O-ACCEL reduces to the Full Orthogonalization Method for linear systems when the objective is quadratic, which differentiates our proposed approach from existing acceleration methods. Comparisons with L-BFGS and N-CG indicate the competitiveness of O-ACCEL. As it can be combined with domain-specific optimizers, it may also be beneficial in areas where L-BFGS or N-CG are not suitable.Comment: 18 pages, 6 figures, 5 table