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

Given a set S of n points in the plane and two directions r/sub 1/ and r/sub 2/, the angle-restricted all nearest neighbor problem (ARANN) asks to compute for every point p in S the nearest point in S lying in the planar region bounded by two rays in the directions r/sub 1/ and r/sub 2/ emanating from p. The ARANN problem generalizes the well-known ANN problem and finds applications to pattern recognition, image processing, and computational morphology. Our main contribution is to present an algorithm that solves an arbitrary instance of size n of the ARANN problem in O(1) time on a reconfigurable mesh of size n/spl times/n. Our algorithm is optimal in the sense that /spl Omega/(n/sup 2/) processors are necessary to solve the ARANN problem in O(1) time.

/pdf/an-optimal-algorithm-for-the-angle-restricted-all-nearest-2j0s62ueeb.pdf

An optimal algorithm for the angle-restricted all nearest neighbor problem on the reconfigurable mesh

The main contribution of this paper is to present a simple exhaustive search algorithm for the quadratic unconstraint binary optimization (QUBO) problem. It computes the values of the objective function E(X) for all n-bit input vector X in O(2
 n
) time. Since Ω(2
 n
) time is necessary to output E(X) for all 2
 n
 vectors X, this sequential algorithm is optimal. We also present a work-time optimal parallel algorithm running O(log n) time using 2
 n
/ log n processors on the CREW-PRAM. This parallel algorithm is work optimal, because the total number of computational operations is equal to the running time of the optimal sequential algorithm. Also, it is time optimal because any parallel algorithm using any large number of processors takes at least Ω(log n) time for evaluating E(X). Further, we have implemented this parallel algorithm to run on the GPU. The experimental results on NVIDIA GeForce RTX 2080Ti GPU show that our GPU implementation runs more than 1000 times faster than the sequential algorithm running on Intel Corei7-8700K CPU(3.70GHz) for the QUBO with nbit vector whenever n ≥ 33. We also compare our exhaustive search parallel algorithm with several non-exhaustive search approaches for solving the QUBO including D-Wave 2000Q quantum annealer, simulated annealing algorithm, and Gurobi optimizer.

A Work-Time Optimal Parallel Exhaustive Search Algorithm for the QUBO and the Ising model, with GPU implementation

Finding a vast array of applications, the list-ranking problem has emerged as one of the fundamental techniques in parallel algorithm design. Surprisingly, the best previously known algorithm to rank a list of n items on a reconfigurable mesh of size \(n \times n\) was running in O(log n ) time. It was open for more than 8 years to obtain a faster algorithm for this important problem.

Efficient List Ranking on the Reconfigurable Mesh, with Applications

An Energy-Efficient Initialization Protocol for Wireless Sensor Networks with No Collision Detection

One of the major challenges in ad hoc networks is to ensure nodal collaboration. Nevertheless, collaboration may lead to undesired results when nodes can exploit their siblings for their own benefits. Until recently, the research community focused on ensuring nodal cooperation at the network layer. In this work we focus on node behavior at the medium access control (MAC) layer. more specifically, this work focus on mechanisms to evaluate nodal activity and verify whether a node is adhering to the protocol rules or not. We show that misconduct at the MAC layer can have serious implications in terms of throughput. Our main contribution is a mechanism that enables nodes to monitor neighboring activity and assess their conduct based on the observed information.

/pdf/mac-layer-misbehavior-on-ad-hoc-networks-yoy5tsrocj.pdf

Koji Nakano

Papers

An optimal algorithm for the angle-restricted all nearest neighbor problem on the reconfigurable mesh

A Work-Time Optimal Parallel Exhaustive Search Algorithm for the QUBO and the Ising model, with GPU implementation

Efficient List Ranking on the Reconfigurable Mesh, with Applications

An Energy-Efficient Initialization Protocol for Wireless Sensor Networks with No Collision Detection

MAC Layer Misbehavior on Ad Hoc Networks