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

Extensive humeral hydatid cyst with extraosseous involvement: a case report

Hydatid cysts caused by Echinococcus species mainly involve visceral organs. Rarely skeletal involvement occurs. The spine and pelvis account for half of the cases of osseous hydatidosis, making humeral hydatid cysts one of the rarest conditions. We report a case of humeral hydatidosis in a 42-year male who presented to us with pain and swelling over the left upper arm, radiological investigations suggestive of osseous cystic lesions were inconclusive and diagnosis of hydatidosis was confirmed with a biopsy subsequently. Surgical excision and curettage of bone and surrounding soft tissue were done, and the void was filled using PMMA cement followed by antihelminthic chemotherapy. No complication or recurrence has been found postoperatively at the end of 6 months of follow-up, with preservation of limb function. To keep orthopedic surgeons aware of this morbid condition, due to its low prevalence, and advanced presentation which is likely misdiagnosed, and even after the early intervention, there is a high recurrence rate which makes this one of the rare cases of humeral hydatidosis notifiable