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

A Broadcast Communication Model (BCM, for short) is a distributed system with no central arbiter populated by n processing units referred to as stations. The stations can communicate by broadcasting/receiving a data packet to one of k distinct communication channels. We assume that the stations run on batteries and expend power while broadcasting/receiving a data packet. Thus, the most important measure to evaluate algorithms on the BCM is the number of awake time slots, in which a station is broadcasting/receiving a data packet. The main contribution of this paper is to present time and energy optimal list ranking algorithms on the BCM. We first show that the rank of every node in an n-node linked list can be determined in O(n) time slots with no station being awake for more than O(1) time slots on the single-channel n-station BCM with no collision detection. We then extend this algorithm to run on the k-channel BCM. For any small fixed ∊>0, our list ranking algorithm runs in time slots with no station being awake for more than O(1) time slots, provided that k≤n1-∊. Clearly, time is necessary to solve the list ranking problem for an n-node linked list on the k-channel BCM. Therefore, our list ranking algorithm on the k-channel BCM is time and energy optimal.

TIME AND ENERGY OPTIMAL LIST RANKING ALGORITHMS ON THE k-CHANNEL BROADCAST COMMUNICATION MODEL WITH NO COLLISION DETECTION

Digital color halftoning is a process to convert a continuous-tone color image into an image with a limited number of colors. This process is re- quired to generate an image reproducing the colors, the tone, and the details of the original continuous- tone color image. An elementary color halftoning method is to apply halftoning techniques indepen- dently to each of the color planes. For example, a full color image is separated into three continuous-tone images with C (Cyan), M (Magenta), and Y (Yellow) process colors, and each of them is independently con- verted to a binary image. Since this method ignores the relation among color planes, three process col- ors are overlapped randomly and it produces noisy and poor printing results. The main contribution of this paper is to present a new color error diffusion method. The key idea of our new method is to uni- formly distribute pixels of 8 combination colors CMY, CM, CY, MY, C, M, Y, and W obtained by combining three process colors C, M, and Y. Also, the bright- ness of the resulting images are equalized using the error diffusion. The experimental results show that our new color halftoning technique generates better quality printing results compared to the independent

/pdf/low-noise-color-error-diffusion-using-the-8-color-planes-4juggfcjib.pdf

Low Noise Color Error Diffusion using the 8-Color Planes

A matrix A of size m/spl times/n containing items from a totally ordered universe is termed monotone if for every i, j, 1/spl les/i 2. Our second contribution is to exhibit a number of non-trivial lower bounds for matrix search problems. These lower bound results hold for arbitrary infinite two-dimensional reconfigurable meshes as long as the input is pretiled onto an n/spl times/n submesh thereof. Specifically, in this context we show that every algorithm that solves the problem of computing the minimum of an n/spl times/n matrix must take /spl Omega/(log log n) time. The same lower bound is shown to hold for the problem of computing the minima in each row of all arbitrary n/spl times/n matrix. As a by product we obtain an /spl Omega/(log log n) time lower bound for the problem of selecting the k-th smallest item in a monotone matrix, thus extending the previously best known lower bound for selection of the reconfigurable mesh. Finally, we show an almost tight /spl Omega/(/spl radic/(log log n)) time lower bound for the task of computing the row minima of a monotone n/spl times/n matrix.

An efficient algorithm for row minima computations in monotone matrices

Consider a set P of points in the plane sorted by χ-coordinate. A point p in P is said to be a proximate point if there exists a point q on the χ-axis such that p is the closest point to q over all points in P. The proximate points problem is to determine all proximate points in P. We propose optimal sequential and parallel algorithms for the proximate points problem. Our sequential algorithm runs in O(n) time. Our parallel algorithms run in O(log log n) time using \(\frac{n}{{\log \log n}}\)Common-CRCW processors, and in O(log n) time using \(\frac{n}{{\log n}}\)EREW processors. We show that both parallel algorithms are work-time optimal; the EREW algorithm is also time-optimal. As it turns out, the proximate points problem finds interesting and highly nontrivial applications to pattern analysis, digital geometry, and image processing.

Optimal Parallel Algorithms for Finding Proximate Points, with Applications (Extended Abstract)

In this paper, we propose a photomosaic generation method by rearranging divided images. In the photomosaic generation, an input image is divided into small subimages and they are rearranged such that the rearranged image reproduces another image given as a target image. Therefore, we can consider this problem as combinatorial optimization to obtain the rearrangement which reproduces approximate images to the target image. Our new idea is that this rearrangement problem is reduced to a minimum weighted bipartite matching problem. By solving the matching problem, we can obtain the best rearrangement image. Although it can generate the most similar photomosaic image, a lot of computing time is necessary. Hence, we propose an approximation method of the photomosaic generation. This approximation method does not obtain the most similar photomosaic image. However, the computing time can be shortened considerably. Additionally, we accelerate the approximation method using the GPU (Graphics Processing Unit). The experimental result shows that the GPU implementation attains a speed-up factor of 25 times over the sequential CPU implementation.

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Koji Nakano

Papers

TIME AND ENERGY OPTIMAL LIST RANKING ALGORITHMS ON THE k-CHANNEL BROADCAST COMMUNICATION MODEL WITH NO COLLISION DETECTION

Low Noise Color Error Diffusion using the 8-Color Planes

An efficient algorithm for row minima computations in monotone matrices

Optimal Parallel Algorithms for Finding Proximate Points, with Applications (Extended Abstract)

Photomosaic Generation by Rearranging Divided Images