The Towers of Hanoi problem is a classical problem in puzzles, games, mathematics, data structures, and algorithms. In this letter, a least memory used algorithm is proposed by combining the source array and target array for comparing the sizes of disk and labeling the disks in the towers of Hanoi problem. As a result, the proposed algorithm reduces the space needed from 2n+2 to n+5, where n represents the disks number.

Let C be a set of colors, and let ω(c) be an integer cost assigned to a color c in C. An edge-coloring of a graph G is to color all the edges of G so that any two adjacent edges are colored with different colors in C. The cost ω(f) of an edge-coloring f of G is the sum of costs ω(f(e)) of colors f(e) assigned to all edges e in G. An edge-coloring f of G is optimal if ω(f) is minimum among all edge-colorings of G. In this paper, we show that the problem of finding an optimal edge-coloring of a tree T can be simply reduced in polynomial time to the minimum weight perfect matching problem for a new bipartite graph constructed from T. The reduction immediately yields an efficient simple algorithm to find an optimal edge-coloring of T in time O(n1.5Δlog(nNω)), where n is the number of vertices in T, Δ is the maximum degree of T, and Nω is the maximum absolute cost |ω(c)| of colors c in C. We then show that our result can be extended for multitrees.

We study problems in computational geometry from the viewpoint of adaptive algorithms. Adaptive algorithms have been extensively studied for the sorting problem, and in this paper we generalize the framework to geometric problems. To this end, we think of geometric problems as permutation (or rearrangement) problems of arrays, and define the "presortedness" as a distance from the input array to the desired output array. We call an algorithm adaptive if it runs faster when a given input array is closer to the desired output, and furthermore it does not make use of any information of the presortedness. As a case study, we look into the planar convex hull problem for which we discover two natural formulations as permutation problems. An interesting phenomenon that we prove is that for one formulation the problem can be solved adaptively, but for the other formulation no adaptive algorithm can be better than an optimal output-sensitive algorithm for the planar convex hull problem. To further pursue the possibility of adaptive computational geometry, we also consider constructing a kd-tree.

Routing is still a challenging issue for wireless sensor networks (WSNs), in particular for WSNs with a non-uniform deployment of nodes. This paper introduces a Node Aggregation Degree-aware Random Routing (NADRR) algorithm for non-uniform WSNs with the help of two new concepts, namely the Local Vertical Aggregation Degree (LVAD) and Local Horizontal Aggregation Degree (LHAD). Our basic idea is to first apply the LVAD and LHAD to determine one size-proper forwarding region (rather than a fixed-size one as in uniform node deployment case) for each node participating in routing, then select the next hop node from the size-proper forwarding region in a probabilistic way, considering both the residual energy and distribution of nodes. In this way, a good adaptability to the non-uniform deployment of nodes can be guaranteed by the new routing algorithm. Extensive simulation results show that in comparison with other classical geographic position based routing algorithms, such as GPSR, TPGF and CR, the proposed NADRR algorithm can result in lower node energy consumption, better balance of node energy consumption, higher routing success rate and longer network lifetime.

Inter-vehicle communication (IVC) system using 700 MHz band to prevent car crashes has been proposed recently. In this paper, we first apply the FDTD method to the analyses of propagation characteristics at an intersection for IVC. We investigate the propagation characteristics considering the electrical conductivities, thickness and windows of building wall and pedestrians. As a result, it is shown that the electrical conductivities and thickness of building wall have a slight influence. In contrast, windows and pedestrians have a great influence on the propagation characteristics. Furthermore, the azimuth delay profiles are obtained by using the MUSIC algorithm.

A two-dimensional filter for photonic label recognition system using time-to-space conversion and delay compensation was designed using Genetic-Algorithms (GA). For four-bit Binary Phase Shift Keying (BPSK) labels at 160 Gbit/s, contrast ratio of the output for eight different labels was improved by optimization of two-dimentional filtering. The contrast ratio of auto-correlation to cross-correlation larger than 2.16 was obtained by computer simulation. This value is 22% larger than the value of 1.77 with the previously reported system using matched filters.

In this paper, we constructed six infinite classes of balanced Boolean functions. These six classes of Boolean functions achieved optimal algebraic degree, optimal algebraic immunity and high nonlinearity. Furthermore, we gave the proof of the lower bound of the nonlinearities of these balanced Boolean functions and proved the better lower bound of nonlinearity for Carlet-Feng's Boolean function.

This paper presents flexible inner-outer Krylov subspace methods, which are implemented using the fast multipole method (FMM) for solving scattering problems with mixed dielectric and conducting object. The flexible Krylov subspace methods refer to a class of methods that accept variable preconditioning. To obtain the maximum efficiency of the inner-outer methods, it is desirable to compute the inner iterations with the least possible effort. Hence, generally, inaccurate matrix-vector multiplication (MVM) is performed in the inner solver within a short computation time. This is realized by using a particular feature of the multipole techniques. The accuracy and computational cost of the FMM can be controlled by appropriately selecting the truncation number, which indicates the number of multipoles used to express far-field interactions. On the basis of the abovementioned fact, we construct a less-accurate but much cheaper version of the FMM by intentionally setting the truncation number to a sufficiently low value, and then use it for the computation of inaccurate MVM in the inner solver. However, there exists no definite rule for determining the suitable level of accuracy for the FMM within the inner solver. The main focus of this study is to clarify the relationship between the overall efficiency of the flexible inner-outer Krylov solver and the accuracy of the FMM within the inner solver. Numerical experiments reveal that there exits an optimal accuracy level for the FMM within the inner solver, and that a moderately accurate FMM operator serves as the optimal preconditioner.

In this paper, we explicitly construct a large class of symmetric Boolean functions on 2k variables with algebraic immunity not less than d, where integer k is given arbitrarily and d is a given suffix of k in binary representation. If let d = k, our constructed functions achieve the maximum algebraic immunity. Remarkably, 2⌊ log2k ⌋ + 2 symmetric Boolean functions on 2k variables with maximum algebraic immunity are constructed, which are much more than the previous constructions. Based on our construction, a lower bound of symmetric Boolean functions with algebraic immunity not less than d is derived, which is 2⌊ log2d ⌋ + 2(k-d+1). As far as we know, this is the first lower bound of this kind.

The wireless robotic sensor network (WRSN) is a combination of a mobile robot and wireless sensor networks. In WRSN, robots perform high-level missions such as human rescue, exploration in dangerous areas, and maintenance and repair of unmanned networks in cooperation with surrounding sensor nodes. In such a network, robots should move to the accident site as soon as possible. This paper proposes a distance-aware robot routing (DAR) algorithm, which focuses on how to pick the shortest path for the mobile robot by considering characteristics different from packet routing. Simulations are performed to demonstrate the benefits of using the proposed algorithm.

This letter presents integrating algorithms for affine constraints defined on a manifold. We first explain definition and geometric representation of affine constraints. Next, we derive integrating algorithms to calculate independent first integrals of affine constraints for the two cases where the they are completely integrable and partially nonintegrable. Moreover, we prove the existence of inverse functions in the algorithms. Some examples are also shown to verify our results.

Recently, pairing-based cryptographic application sch-emes have attracted much attentions. In order to make the schemes more efficient, not only pairing algorithm but also arithmetic operations in extension field need to be efficient. For this purpose, the authors have proposed a series of cyclic vector multiplication algorithms (CVMAs) corresponding to the adopted bases such as type-I optimal normal basis (ONB). Note here that every basis adapted for the conventional CVMAs are just special classes of Gauss period normal bases (GNBs). In general, GNB is characterized with a certain positive integer h in addition to characteristic p and extension degree m, namely type-⟨h.m⟩ GNB in extension field Fpm. The parameter h needs to satisfy some conditions and such a positive integer h infinitely exists. From the viewpoint of the calculation cost of CVMA, it is preferred to be small. Thus, the minimal one denoted by hmin will be adapted. This paper focuses on two remaining problems: 1) CVMA has not been expanded for general GNBs yet and 2) the minimal hmin sometimes becomes large and it causes an inefficient case. First, this paper expands CVMA for general GNBs. It will improve some critical cases with large hmin reported in the conventional works. After that, this paper shows a theorem that, for a fixed prime number r, other prime numbers modulo r uniformly distribute between 1 to r-1. Then, based on this theorem, the existence probability of type-⟨hmin,m⟩ GNB in Fpm and also the expected value of hmin are explicitly given.

Accurate registration is crucial for medical image analysis. In this letter, we proposed an improved Demons technique (IDT) for medical image registration. The IDT improves registration quality using orthogonal gradient information. The advantage of the proposed IDT is assessed using 14 medical image pairs. Experimental results show that the proposed technique provides about 8% improvement over existing Demons-based techniques in terms of registration accuracy.

In this paper, we discuss the parallel degree of well-structured workflow nets, WF-nets, for short. First, we give the definition of parallel degree, PARAdeg, for WF-nets. Second, we show it is intractable to compute the value of PARAdeg for acyclic well-structured WF-nets. Next we construct two heuristic algorithms to compute the value. The first algorithm is focused on nest structure and the second one is focused on the longest path. Finally, we perform an experiment to compare the two algorithms and the result is that the accuracy of the first algorithm based on nest structure was higher than that of the second one based on the longest path for most well-structured WF-nets and the accuracy of the second one is better than that of first one only when the well-structured workflow nets are mainly composed by the parallel structures.

To reduce the manufacturing cost of SoCs with many embedded SRAMs, we propose a scheme to reduce the area per good die for the SoC memory built-in self-test (MBIST). We first propose BIST hardware overhead reduction by application of an encoder-based comparator. For the repair of a faulty SRAM module with 2-D redundancy, we propose spare assignement algorithm. Based on an existing range-cheking-first algorithm (RCFA), we propose assign-all-row-RCFA (A-RCFA) which assign unused spare rows to faulty ones, in order to suppress the degradation of repair rate due to compressed fail location information output from the encoder-based comparator. Then, considering that an SoC has many SRAM modules, we propose a heuristic algorithm based on iterative improvement algorithm (IIA), which determines whether each SRAM should have a spare row or not, in order to minimize area per a good die. Experimental results on practical scale benchmark SoCs with more than 1,000 SRAM modules indicate that encoder-based comparators reduce hardware overhead by about 50% compared to traditional ones, and that combining the IIA-based algorithm for determining redundancy architecture with the encoder-based comparator effectively reduces the area per good die.

Base station (BS) cooperation is a promising technique to suppress co-channel interference for cellular networks. However, practical limitations constrain the scale of cooperation, thus the network is divided into small disjoint BS cooperation groups, namely clusters. A decentralized scheme for BS cluster formation is proposed based on efficient BS negotiations, of which the feedback overhead per user is nearly irrelevant to the network size, and the number of iteration rounds scales very slowly with the network size. Simulations show that our decentralized scheme provides significant sum-rate gain over static clustering and performs almost the same as the existing centralized approach. The proposed scheme is well suited for large-scale cellular networks due to its low overhead and complexity.

Recently, Mooij et al. proposed new sufficient conditions for convergence of the sum-product algorithm, and it was also shown that if the factor graph is a tree, Mooij's sufficient condition for convergence is always activated. In this letter, we show that the converse of the above statement is also true under some assumption, and that the assumption holds for the sum-product decoding. These newly obtained fact implies that Mooij's sufficient condition for convergence of the sum-product decoding is activated if and only if the factor graph of the a posteriori probability of the transmitted codeword is a tree.

We propose an "estimation of distribution algorithm" incorporating switching. The algorithm enables switching from the standard estimation of distribution algorithm (EDA) to the genetic algorithm (GA), or vice versa, on the basis of switching criteria. The algorithm shows better performance than GA and EDA in deceptive problems.

We consider the backlight calculation of local dimming as an optimization problem. The luminance produced by many LEDs at each pixel considered is calculated which should cover the gray value of each pixel, while the sum of LED currents is to be minimized. For this purpose a specific approach called as "Sorted Sector Covering" (SSC) was developed and is described in this paper. In our pre-processing unit called condenser the source image is reduced to a matrix of much lower resolution so that the computation effort of the SSC algorithm is drastically reduced. During this preprocessing phase, filter functions can be integrated so that a further reduction of the power consumption is achieved. Our processing system allows high power saving and high visual quality at low processor cost. We approach the local dimming problem in the physical viewing direction -- from LED to pixel. The luminance for the pixel is based on the light spread function (LSF) and the PWM values of the LEDs. As the physical viewing direction is chosen, this method is universal and can be applied for any kind of LED arrangement -- direct-lit as well as edge-lit. It is validated on prototypes, e.g., a locally dimmed edge-lit TV.

In this work, a high performance LDPC decoder architecture is presented. It is a partially-parallel architecture for low-complexity consideration. In order to eliminate the idling time and hardware complexity in conventional partially-parallel decoders, the decoding process, decoder architecture and memory structure are optimized. Particularly, the parity-check matrix is optimally partitioned into four unequal sub-matrices that lead to high efficiency in hardware sharing. As a result, it can handle two different codewords simultaneously with 100% hardware utilization. Furthermore, for minimizing the performance loss due to round-off errors in fixed-point implementations, the well-known modified min-sum decoding algorithm is enhanced by our recently proposed high-performance CMVP decoding algorithm. Overall, the proposed decoder has high throughput, low complexity, and good BER performances. In the circuit implementation example of the (576,288) parity check matrix for IEEE 802.16e standard, the decoder achieves a data rate of 5.5 Gbps assuming 10 decoding iterations and 7 quantization bits, with a small area of 653 K gates, based on UMC 90 nm process technology.