There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

We have witnessed great interest and a wealth of promise in content-based image retrieval as an emerging technology. While the last decade laid foundation to such promise, it also paved the way for a large number of new techniques and systems, got many new people involved, and triggered stronger association of weakly related fields. In this article, we survey almost 300 key theoretical and empirical contributions in the current decade related to image retrieval and automatic image annotation, and in the process discuss the spawning of related subfields. We also discuss significant challenges involved in the adaptation of existing image retrieval techniques to build systems that can be useful in the real world. In retrospect of what has been achieved so far, we also conjecture what the future may hold for image retrieval research.

/pdf/image-retrieval-ideas-influences-and-trends-of-the-new-age-51whw4w7su.pdf

Image retrieval: Ideas, influences, and trends of the new age

Computational geometry

Ad hoc networks are self-organizing entities that are deployed on demand in support of various events including collaborative computing, multimedia classroom, disaster-relief, search-and-rescue, interactive mission planning, and law enforcement operations. One of the fundamental tasks that have to be addressed when setting up an ad hoc network (AHN, for short) is initialization. This involves assigning each of the n stations in the AHN a distinct ID number (e.g., a local IP address) in the range from 1 to n. Our main contribution is to propose efficient randomized initialization protocols for AHNs. We begin by showing that if the number n of stations is known beforehand, an n-station, single-channel AHN can be initialized with probability exceeding 1-(1/n), in en+O(/spl radic/(nlogn)) time slots, regardless of whether the AHN has collision detection capability. We then go on to show that even if n is not known in advance, an n-station, single-channel AHN with collision detection can be initialized with probability exceeding 1-(1/n), in (10n)/3+O(/spl radic/(n 1n n)) time slots. Using this protocol as a stepping stone, we then present an initialization protocol for the n-station, k-channel AHN with collision detection that terminates with probability exceeding 1-(1/n), in (10n)/(3k)+O(/spl radic/(n 1n n)/k) time slots. Finally, we look at the case where the collision detection capability is not present. Our first result in this direction is to show that the task of electing a leader in an n-station, single-channel AHN can be completed with probability exceeding 1-(1/n), in fewer than 11.37(iog n)/sup 2/+2.39 log n time slots. This leader election protocol allows us to design an initialization protocol for the n-station, single-channel AHN with no collision detection that terminates with probability exceeding 1-(1/n), in fewer than 5.67n+O(/spl radic/(n 1n n)) time slots, even if n is not known beforehand. We then discuss an initialization protocol for the n-station, k-channel AHN with no collision detection that terminates with probability exceeding 1-(1/n), in fewer than 5.67(n/k)+O(/spl radic/(n 1n n)/k) time slots, whenever k/spl les/n/((log n)/sup 3/).

Randomized initialization protocols for ad hoc networks

A radio network is a distributed system with no central arbiter, consisting of n radio transceivers, henceforth referred to as stations. We assume that the stations are identical and cannot be distinguished by serial or manufacturing number. The leader election problem asks to designate one of the stations as leader. In this work, we focus on single-channel, single-hop radio networks. We assume that time is slotted and all transmissions occur at slot boundaries. In each time slot, the stations transmit on the channel with some probability until, eventually, one of the stations is declared leader. A leader election protocol is said to be uniform if, in each time slot, every station transmits with the same probability. In a seminal paper, Willard (1986) presented a uniform leader election protocol for single-channel single-hop radio stations terminating in log log n+o(log log n) expected time slots. It was open for more than 15 years whether Willard's protocol featured the same time performance with "high probability." One of our main contributions is to show that, unfortunately, this is not the case. Specifically, we prove that for every parameter f/spl isin/e/sup O(n)/, in order to ensure termination with probability exceeding 1-1/f, Willard's protocol must take log log n+/spl Omega/(/spl radic/f) time slots. The highlight of this work is a novel uniform leader election protocol that terminates, with probability exceeding 1-1/f, in log log n+o(log log n)+O(log f) time slots. Finally, we provide simulation results that show that our leader election protocol outperforms Willard's protocol in practice.

/pdf/uniform-leader-election-protocols-for-radio-networks-3p0w11ojhf.pdf

Uniform leader election protocols for radio networks

Recent GPUs, which have many processing units connected with a global memory, can be used for general purpose parallel computation. Users can develop parallel programs running on GPUs using programming architecture called CUDA (Compute Unified Device Architecture). The main contribution of this paper is to implement a Canny edge detection algorithm on CUDA. The experimental result shows that our implementation of Canny edge detection algorithm on CUDA achieves a speedup factor of 61 over a conventional software implementation.

Efficient Canny Edge Detection Using a GPU

Given a 2-D binary image of size n×n, Euclidean Distance Map (EDM) is a 2-D array of the same size such that each element is storing the Euclidean distance to the nearest black pixel. It is known that a sequential algorithm can compute the EDM in O(n2) and thus this algorithm is optimal. Also, work-time optimal parallel algorithms for shared memory model have been presented. However, the presented parallel algorithms are too complicated to implement in existing shared memory parallel machines. The main contribution of this paper is to develop a simple parallel algorithm for the EDM and implement it in two different parallel platforms: multicore processors and Graphics Processing Units (GPUs). We have implemented our parallel algorithm in a Linux server with four Intel hexad-core processors (Intel Xeon X7460 2.66GHz). We have also implemented it in the following two modern GPU systems, Tesla C1060 and GTX 480, respectively. The experimental results have shown that, for an input binary image with size of 9216×9216, our implementation in the multicore system achieves a speedup factor of 18 over the performance of a sequential algorithm using a single processor in the same system. Meanwhile, for the same input binary image, our implementation on the GPU achieves a speedup factor of 26 over the sequential algorithm implementation.

/pdf/implementations-of-a-parallel-algorithm-for-computing-26qarnahca.pdf

Implementations of a Parallel Algorithm for Computing Euclidean Distance Map in Multicore Processors and GPUs

The main contribution of this work is to propose energy-efficient randomized leader election protocols for single-hop, single-channel radio networks (RN) that do not have collision detection (CD) capabilities We first presents a leader election protocol for the case the number n of stations is known beforehand The protocol runs in O(log f) time slots with no station being awake for more than O(log log f + log f/log n) time slots with probability at least 1 - 1/f for any f ≥ 1 We then present three leader election protocols for the case where n is not known beforehand The first protocol terminates, with probability exceeding 1 - 1/f, in O((log n)2 + (log f)2) time slots, with no station being awake for more than O(log n + log f) time slots Clearly, this first protocol terminates in O((log n)2) expected time slots Our second protocol reduces the expected termination time to O(log n) time slots This second protocol terminates, with probability exceeding 1 - 1/f in O(f3/5 log n) time slots Finally, by combining these two protocols, we obtain a third leader election protocol that terminates in O(log n) expected time slots This latter protocol terminates, with with probability exceeding 1 - 1/f, in O(min((log n)2 + (log f)2, f3/5log n)) time slots, with no station being awake for more than O(log n + log f) time slots

Koji Nakano

Papers

Randomized initialization protocols for ad hoc networks

Uniform leader election protocols for radio networks

Efficient Canny Edge Detection Using a GPU

Implementations of a Parallel Algorithm for Computing Euclidean Distance Map in Multicore Processors and GPUs

Randomized Leader Election Protocols in Radio Networks with No Collision Detection