A New Push-Relabel Algorithm for Sparse Networks

In this paper, we present a new push-relabel algorithm for the maximum flow problem on flow networks with $n$ vertices and $m$ arcs. Our algorithm computes a maximum flow in $O(mn)$ time on sparse networks where $m = O(n)$. To our knowledge, this is the first $O(mn)$ time push-relabel algorithm for the $m = O(n)$ edge case; previously, it was known that push-relabel implementations could find a max-flow in $O(mn)$ time when $m = \Omega(n^{1+\epsilon})$ (King, et. al., SODA `92). This also matches a recent flow decomposition-based algorithm due to Orlin (STOC `13), which finds a max-flow in $O(mn)$ time on sparse networks. Our main result is improving on the Excess-Scaling algorithm (Ahuja & Orlin, 1989) by reducing the number of nonsaturating pushes to $O(mn)$ across all scaling phases. This is reached by combining Ahuja and Orlin's algorithm with Orlin's compact flow networks. A contribution of this paper is demonstrating that the compact networks technique can be extended to the push-relabel family of algorithms. We also provide evidence that this approach could be a promising avenue towards an $O(mn)$-time algorithm for all edge densities.Comment: 23 pages. arXiv admin note: substantial text overlap with arXiv:1309.2525 - This version includes an extension of the result to the O(n) edge cas

2048 is (PSPACE) Hard, but Sometimes Easy

We prove that a variant of 2048, a popular online puzzle game, is PSPACE-Complete. Our hardness result holds for a version of the problem where the player has oracle access to the computer player's moves. Specifically, we show that for an $n \times n$ game board $\mathcal{G}$, computing a sequence of moves to reach a particular configuration $\mathbb{C}$ from an initial configuration $\mathbb{C}_0$ is PSPACE-Complete. Our reduction is from Nondeterministic Constraint Logic (NCL). We also show that determining whether or not there exists a fixed sequence of moves $\mathcal{S} \in \{\Uparrow, \Downarrow, \Leftarrow, \Rightarrow\}^k$ of length $k$ that results in a winning configuration for an $n \times n$ game board is fixed-parameter tractable (FPT). We describe an algorithm to solve this problem in $O(4^k n^2)$ time.Comment: 13 pages, 11 figure

K-Shell Ionization Measurements for Light Incident Icons

The ionization of the K-shell in targets of copper, silver, dysprosium and gold was investigated with incident ion beams of proton and helium ions in the range 0.5 MeV/u to 3 MeV/u. The x-rays were detected by a HpGe detector. K-shell x-ray production cross section were determined by normalization of the x-ray yield to the incident beam flux, the Rutherford-scattered ions and the nuclear-Coulomb excited gamma ray yield. The multiple normalization procedures minimize the errors in these cross section measurements. The data are compared with the predictions of the ECPSSR theory for K-shell ionization. The atomic number dependence of these K-shell cross section is discussed

ZERO-DOWNTIME ZERO-DATA LOSS UPGRADE FOR APPLICATION AGENTS

An agent architecture is provided that allows for the agent to be upgraded on the fly with a single click. This architecture works regardless of the deployment strategy in use in a customer\u27s environment, the technology stack in use, and how large or small the change in the agent might be. The architecture may help to save a significant amount of time for the customer to maintain the agent versions and provide easier options to change the agent\u27s behavior in case something goes wrong (with respect to functionality or security) within seconds. Further, the architecture may help to save vendors significant effort that would otherwise be needed to enable, support, and keep up with the new deployment strategies that might come up over time