We consider the computation of r-th roots in finite fields. For the computation of square roots (i.e., the case of r=2), there are two typical methods: the Tonelli-Shanks method [7],[10] and the Cipolla-Lehmer method [3],[5]. The former method can be extended to the case of r-th roots with r prime, which is called the Adleman-Manders-Miller method [1]. In this paper, we generalize the Cipolla-Lehmer method to the case of r-th roots in Fq with r prime satisfying r | q-1, and provide an efficient computational procedure of our method. Furthermore, we implement our method and the Adleman-Manders-Miller method, and compare the results.

This paper presents an efficient algorithm for reporting all intersections among n given segments in the plane using work space of arbitrarily given size. More exactly, given a parameter s which is between Ω(1) and O(n) specifying the size of work space, the algorithm reports all the segment intersections in roughly O(n2/+ K) time using O(s) words of O(log n) bits, where K is the total number of intersecting pairs. The time complexity can be improved to O((n2/s) log s + K) when input segments have only some number of different slopes.

Many problems can be formulated as maximum clique problems. Hence, it is highly important to develop algorithms that can find a maximum clique very fast in practice. We propose new approximate coloring and other related techniques which markedly improve the run time of the branch-and-bound algorithm MCR (J. Global Optim., 37, pp.95–111, 2007), previously shown to be the fastest maximum-clique-finding algorithm for a large number of graphs. The algorithm obtained by introducing these new techniques in MCR is named MCS. It is shown that MCS is successful in reducing the search space quite efficiently with low overhead. Extensive computational experiments confirm the superiority of MCS over MCR and other existing algorithms. It is faster than the other algorithms by orders of magnitude for several graphs. In particular, it is faster than MCR for difficult graphs of very high density and for very large and sparse graphs, even though MCS is not designed for any particular type of graph. MCS can be faster than MCR by a factor of more than 100,000 for some extremely dense random graphs. This paper demonstrates in detail the effectiveness of each new techniques in MCS, as well as the overall contribution.

We humans are easily able to instantaneously detect the regions in a visual scene that are most likely to contain something of interest. Exploiting this pre-selection mechanism called visual attention for image and video processing systems would make them more sophisticated and therefore more useful. This paper briefly describes various computational models of human visual attention and their development, as well as related psychophysical findings. In particular, our objective is to carefully distinguish several types of studies related to human visual attention and saliency as a measure of attentiveness, and to provide a taxonomy from several viewpoints such as the main objective, the use of additional cues and mathematical principles. This survey finally discusses possible future directions for research into human visual attention and saliency computation.

We study the computational complexity of the following two-player game. The instance is a graph G = (V,E), an initial vertex s ∈ V, and a target set T ⊆ V. A “cat” is initially placed on s. Player 1 chooses a vertex in the graph and removes it and its incident edges from the graph. Player 2 moves the cat from the current vertex to one of the adjacent vertices. Players 1 and 2 alternate removing a vertex and moving the cat, respectively. The game continues until either the cat reaches a vertex of T or the cat cannot be moved. Player 1 wins if and only if the cat cannot be moved before it reaches a vertex of T. It is shown that deciding whether player 1 has a forced win on the game on G is PSPACE-complete.

We present an Interactive Tabu Search (ITS) algorithm to reduce the evaluation load of Interactive Evolutionary Computation (IEC) users. Most previous IEC studies used an evaluation interface that required users to provide evaluation values for all candidate solutions. However, user's burden with such an evaluation interface is large. Therefore, we propose ITS where users choose the favorite candidate solution from the presented candidate solutions. Tabu Search (TS) is recognized as an optimization technique. ITS evaluation is simpler than Interactive Genetic Algorithm (IGA) evaluation, in which users provide evaluation values for all candidate solutions. Therefore, ITS is effective for reducing user evaluation load. We evaluated the performance of our proposed ITS and a Normal IGA (NIGA), which is a conventional 10-stage evaluation, using a numerical simulation with an evaluation agent that imitates human preferences (Kansei). In addition, we implemented an ITS evaluation for a running-shoes-design system and examined its effectiveness through an experiment with real users. The simulation results showed that the evolution performance of ITS is better than that of NIGA. In addition, we conducted an evaluation experiment with 21 subjects in their 20 s to assess the effectiveness of these methods. The results showed that the satisfaction levels for the candidates generated by ITS and NIGA were approximately equal. Moreover, it was easier for test subjects to evaluate candidate solutions with ITS than with NIGA.

This paper presents an efficient approach for logarithmic and anti-logarithmic converters which can be used in the arithmetic unit of hybrid number system processors and logarithm/exponent function generators in DSP applications. By employing the novel quasi-symmetrical difference method with only the simple shift-add logic and the look-up table, the proposed approach can reduce the hardware area and improve the conversion speed significantly while achieve similar accuracy compared with the previous methods. The implementation results in both FPGA and 0.18-µm CMOS technology are also presented and discussed.

Blocking artifacts are introduced in many block-based coding systems, and its reduction can significantly improve the subjective quality of compressed video. The H.264/AVC uses an in-loop deblocking filter to remove the blocking artifacts. The filter considers some coding conditions in its adaptive deblocking filtering such as coded block pattern (CBP), motion vector, macroblock type, etc. for inter-predicted blocks, however, it does not consider much for intra-coded blocks. In this paper, we utilize the human visual system (HVS) characteristic and the local characteristic of image blocks to modify the boundary strength (BS) of the intra-deblocking filter in order to gain improvement in the subjective quality and also to reduce the complexity in filtering intra coded slices. In addition, we propose a low-complexity deblocking method which utilizes the correlation between vertical and horizontal boundaries of a block in inter coded slices. Experimental results show that our proposed method achieves not only significant gain in the subjective quality but also some PSNR gain, and reduces the computational complexity of the deblocking filter by 36.23% on average.

In this paper we study quantum nondeterminism in multiparty communication. There are three (possibly) different types of nondeterminism in quantum computation: i) strong, ii) weak with classical proofs, and iii) weak with quantum proofs. Here we focus on the first one. A strong quantum nondeterministic protocol accepts a correct input with positive probability and rejects an incorrect input with probability 1. In this work we relate strong quantum nondeterministic multiparty communication complexity to the rank of the communication tensor in the Number-On-Forehead and Number-In-Hand models. In particular, by extending the definition proposed by de Wolf to nondeterministic tensor-rank (nrank), we show that for any boolean function f when there is no prior shared entanglement between the players, 1) in the Number-On-Forehead model the cost is upper-bounded by the logarithm of nrank(f); 2) in the Number-In-Hand model the cost is lower-bounded by the logarithm of nrank(f). Furthermore, we show that when the number of players is o(log log n), we have NQP BQP for Number-On-Forehead communication.

Given an integer n-dimensional lattice basis, the random sampling reduction was proven to find a short vector in arithmetic steps with an integer k, which is freely chosen by users. This paper introduces new random sampling reduction using precomputation techniques. The computation cost is almost independent of the lattice dimension number. The new method is therefore especially advantageous to find a short lattice vector in higher dimensions. The arithmetic operation number of our new method is about 20% of the random sampling reduction with 200 dimensions, and with 1000 dimensions it is less than 1% ( 1/130) of that of the random sampling reduction with representative parameter settings under reasonable assumptions.

Dynamic Programming (DP) based Track-Before-Detect (TBD) algorithm is effective in detecting low signal-to-noise ratio (SNR) targets. However, its complexity increases exponentially as the dimension of the target state space increases, so the exact implementation of DP-TBD will become computationally prohibitive if the state dimension is more than two or three, which greatly prevents its applications to many realistic problems. In order to improve the computational efficiency of DP-TBD, a thresholding process based DP-TBD (TP-DP-TBD) is proposed in this paper. In TP-DP-TBD, a low threshold is first used to eliminate the noise-like (with low-amplitude) measurements. Then the DP integration process is modified to only focuses on the thresholded higher-amplitude measurements, thus huge amounts of computation devoted to the less meaningful low-amplitude measurements are saved. Additionally, a merit function transfer process is integrated into DP recursion to guarantee the inheritance and utilization of the target merits. The performance of TP-DP-TBD is investigated under both optical style Cartesian model and surveillance radar model. The results show that substantial computation reduction is achieved with limited performance loss, consequently TP-DP-TBD provides a cost-efficient tradeoff between computational cost and performance. The effect of the merit function transfer on performance is also studied.

Secret sharing schemes have been proposed to protect content by dividing it into many pieces securely and distributing them over different locations. Secret sharing schemes can also be used for the secure delivery of content. The original content cannot be reconstructed by the attacker if the attacker cannot eavesdrop on all the pieces delivered from multiple content servers. This paper aims to obtain secure delivery routes for the pieces, which minimizes the probability that all the pieces can be stolen on the links composing the delivery routes. Although such a route optimization problem can be formulated using an ILP (Integer Linear Programming) model, optimum route computation based on the ILP model requires large amounts of computational resources. Thus, this paper proposes a lightweight route computation method for obtaining suboptimum delivery routes that achieve a sufficiently small probability of all the pieces being stolen. The proposed method computes the delivery routes successively by using the conventional shortest route algorithm repeatedly. The distance of the links accommodating the routes that have already been calculated is adjusted iteratively and utilized for calculation of the new shortest route. The results of a performance evaluation clarify that sufficiently optimum routes can be computed instantly even in practical large-scale networks by the proposed method, which adjusts the link distance strictly based on the risk level at the considered link.

Shisen-Sho is a tile-based one-player game. The instance is a set of 136 tiles embedded on 817 rectangular grids. Two tiles can be removed if they are labeled by the same number and if they are adjacent or can be connected with at most three orthogonal line segments. Here, line segments must not cross tiles. The aim of the game is to remove all of the 136 tiles. In this paper, we consider the generalized version of Shisen-Sho, which uses an arbitrary number of tiles embedded on rectangular grids. It is shown that deciding whether the player can remove all of the tiles is NP-complete.

Computational Fluid Dynamics (CFD) is used as a common design tool in the aerospace industry. UPACS, a package for CFD, is convenient for users, since a customized simulator can be built just by selecting desired functions. The problem is its computation speed, which is difficult to enhance by using the clusters due to its complex memory access patterns. As an economical solution, accelerators using FPGAs are hopeful candidate. However, the total scale of UPACS is too large to be implemented on small numbers of FPGAs. For cost efficient implementation, partial reconfiguration which dynamically loads only required functions is proposed in this paper. Here, the MUSCL scheme, which is used frequently in UPACS, is selected as a target. Partial reconfiguration is applied to the flux limiter functions (FLF) in MUSCL. Four FLFs are implemented for Turbulence MUSCL (TMUSCL) and eight FLFs are for Convection MUSCL (CMUSCL). All FLFs are developed independently and separated from the top MUSCL module. At start-up, only required FLFs are selected and deployed in the system without interfering the other modules. This implementation has successfully reduced the resource utilization by 44% to 63%. Total power consumption also reduced by 33%. Configuration speed is improved by 34-times faster as compared to full reconfiguration method. All implemented functions achieved at least 17 times speed-up performance compared with the software implementation.

It is becoming more and more important to make use of personal or classified information while keeping it confidential. A promising tool for meeting this challenge is secure multi-party computation (MPC). It enables multiple parties, each given a snippet of a secret s, to compute a function f(s) by communicating with each other without revealing s. However, one of the biggest problems with MPC is that it requires a vast amount of communication. Much research has gone into making each protocol (equality testing, interval testing, etc.) more efficient. In this work, we make a set of multiple protocols more efficient by transforming them into their equivalent batch processing form and propose two protocols: “Batch Logical OR” and “Batch Logical AND.” Using proposed protocols recursively, we also propose “Batch Logical OR-AND” and “Batch Logical AND-OR,” and show arbitrary formula consisting of Boolean protocols, OR gates, and AND gates can be batched. Existing logical OR and logical AND protocols consisting of t equality testing invocations have a communication complexity of O(t), where is the bit length of the secrets. Our batched versions of these protocols reduce it to O( + t). For t interval testing invocations, they reduce both communication and round complexity. Thus they can make the queries on a secret shared database more efficient. For example, the use of the proposed protocols reduces the communication complexity for a query consisting of equality testing and interval testing by approximately 70% compared to the use of the corresponding existing protocols. The concept of the proposed protocols is versatile and can be applied to logical formulae consisting of protocols other than equality testing and interval testing, thereby making them more efficient as well.

To reduce the cost of fault management in all-optical networks, it is a promising approach to detect the degradation of optical signal quality solely at the terminal points of all-optical monitoring paths. The all-optical monitoring paths must be routed so that all single-link failures can be localized using route information of monitoring paths where signal quality degradation is detected. However, route computation for the all-optical monitoring paths that satisfy the above condition is time consuming. This paper proposes a procedure for deriving the lower bounds of the required number of monitoring paths to localize all single-link failures, and proposes an efficient monitoring path computation method based on the derived lower bounds. The proposed method repeats the route computation for the monitoring paths until feasible routes can be found, while the assumed number of monitoring paths increases, starting from the lower bounds. With the proposed method, the minimum number of monitoring paths with the overall shortest routes can be obtained quickly by solving several small-scale integer linear programming problems when the possible terminal nodes of monitoring paths are arbitrarily given. Thus, the proposed method can minimize the required number of monitors for detecting the degradation of signal quality and the total overhead traffic volume transferred through the monitoring paths.

A conical area evolutionary algorithm (CAEA) is presented to further improve computational efficiencies of evolutionary algorithms for bi-objective optimization. CAEA partitions the objective space into a number of conical subregions and then solves a scalar subproblem in each subregion that uses a conical area indicator as its scalar objective. The local Pareto optimality of the solution with the minimal conical area in each subregion is proved. Experimental results on bi-objective problems have shown that CAEA offers a significantly higher computational efficiency than the multi-objective evolutionary algorithm based on decomposition (MOEA/D) while CAEA competes well with MOEA/D in terms of solution quality.

This paper presents a novel algorithm to generate homogeneous superpixels from Markov random walks. We exploit Markov clustering (MCL) as the methodology, a generic graph clustering method based on stochastic flow circulation. In particular, we introduce a graph pruning strategy called compact pruning in order to capture intrinsic local image structure. The resulting superpixels are homogeneous, i.e. uniform in size and compact in shape. The original MCL algorithm does not scale well to a graph of an image due to the square computation of the Markov matrix which is necessary for circulating the flow. The proposed pruning scheme has the advantages of faster computation, smaller memory footprint, and straightforward parallel implementation. Through comparisons with other recent techniques, we show that the proposed algorithm achieves state-of-the-art performance.

A packet network architecture called “functionally distributed transport networking” is being studied, where control elements (CEs) are separated from the forwarding elements (FEs) of all routers in a network, and a centralized CE manages the control functions for all FEs. A crucial issue to be addressed in this network architecture is the occurrence of bottlenecks in the CE performance, and rapid network restoration after failures is the main problem to be solved. Thus, we propose here a fast backup route determination method suitable for this network architecture, and we also show the practicality of this architecture. Most failures can be categorized as single-node or single-link failures. The proposed method prepares backup routes for all possible single-node failures in advance and computes backup routes for single-link failures after the failure occurs. The number of possible single-node failures is much less than that of possible single-link failures, and the preparation of backup routes for single-node failures is practical under the memory requirements. Two techniques are used in computing backup routes for single-link failures in order to reduce the computation time. One is to calculate only the routes affected by the link failure. The other is to use an algorithm to compute backup routes for single-link failures based on preplanned backup routes for single-node failures. To demonstrate the practicality of our method, we evaluated the amount of memory and computation time needed to prepare backup routes for all single-node failures, and we carried out simulations with various network topologies to evaluate the route computation time required for a single-link failure.

In this paper, an improved hybrid LUT-based architecture for low-error and efficient fixed-width squarer circuits is presented in which LUT-based and conventional logic circuits are employed together to achieve the good trade-off between hardware complexity and performance. By exploiting the mathematical identities and hybrid architecture, the mean error and mean squarer error of the proposed squarer are reduced by up to 40%, compared with the best previous method presented in literature. Moreover, the proposed method can improve the speed and reduce the area of the squarer circuit. The implementation and chip measurement results in 0.18-µm CMOS technology are also presented and discussed.