The multiple traveling salesman problem (mTSP) is a generalization of the well-known traveling salesman problem (TSP), where more than one salesman is allowed to be used in the solution. Moreover, the characteristics of the mTSP seem more appropriate for real-life applications, and it is also possible to extend the problem to a wide variety of vehicle routing problems (VRPs) by incorporating some additional side constraints. Although there exists a wide body of the literature for the TSP and the VRP, the mTSP has not received the same amount of attention. The purpose of this survey is to review the problem and its practical applications, to highlight some formulations and to describe exact and heuristic solution procedures proposed for this problem.

The multiple traveling salesman problem : an overview of formulations and solution procedures

This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into historical perspective. A summary of the insights and recommendations that follow from relatively recent theoretical as well as experimental studies concludes the presentation.

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Prolog to a chronology of interpolation: from ancient astronomy to modern signal and image processing

We present the design, implementation, and application of several families of fast multiplierless approximations of the discrete cosine transform (DCT) with the lifting scheme called the binDCT. These binDCT families are derived from Chen's (1977) and Loeffler's (1989) plane rotation-based factorizations of the DCT matrix, respectively, and the design approach can also be applied to a DCT of arbitrary size. Two design approaches are presented. In the first method, an optimization program is defined, and the multiplierless transform is obtained by approximating its solution with dyadic values. In the second method, a general lifting-based scaled DCT structure is obtained, and the analytical values of all lifting parameters are derived, enabling dyadic approximations with different accuracies. Therefore, the binDCT can be tuned to cover the gap between the Walsh-Hadamard transform and the DCT. The corresponding two-dimensional (2-D) binDCT allows a 16-bit implementation, enables lossless compression, and maintains satisfactory compatibility with the floating-point DCT. The performance of the binDCT in JPEG, H.263+, and lossless compression is also demonstrated.

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Fast multiplierless approximations of the DCT with the lifting scheme

The Self-Organizing Map (SOM) algorithm has attracted an ever increasing amount of interest among researches and practitioners in a wide variety of elds The SOM and a variant of it, the LVQ, have been analyzed extensively, a number of variants of them have been developed and, perhaps most notably, they have been applied extensively within elds ranging from engineering sciences to medicine, biology, and economics We have collected a comprehensive list of 3343 scienti c papers that use the algorithms, have bene ted from them, or contain analyses of them The list is intended to serve as a source for literature surveys We have provided both a thematic and a keyword index to help nding articles of interest

Bibliography of Self-Organizing Map (SOM) Papers: 1981-1997

1.1 Origin The traveling salesman problem (TSP) were studied in the 18th century by a mathematician from Ireland named Sir William Rowam Hamilton and by the British mathematician named Thomas Penyngton Kirkman. Detailed discussion about the work of Hamilton & Kirkman can be seen from the book titled Graph Theory (Biggs et al. 1976). It is believed that the general form of the TSP have been first studied by Kalr Menger in Vienna and Harvard. The problem was later promoted by Hassler, Whitney & Merrill at Princeton. A detailed dscription about the connection between Menger & Whitney, and the development of the TSP can be found in (Schrijver, 1960).

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Traveling Salesman Problem: an Overview of Applications, Formulations, and Solution Approaches

A neural network approach based on the self-organized feature map model is proposed to solve the multiple traveling salesmen problem (MTSP). Instead of studying the MTSP theoretically, the authors try to solve the MTSP. The process of evolving populations of cells, featuring duplication and selection, iteratively organizes a quasi-optimal solution for each TSP. The example of Wacholder's demonstration is examined. >

A study of feature-mapped approach to the multiple travelling salesmen problem

The mechanisms of acupuncture remain poorly understood, but it is generally assumed that measuring the electrical conductivity at various meridians provides data representing various meridian energies. In the past, noninvasive methods have been used to stimulate the acupuncture points at meridians, such as heat, electricity, magnets, and lasers. Photoluminescent bioceramic (PLB) material has been proven to weaken hydrogen bonds and alter the characteristics of liquid water. In this study, we applied the noninvasive PLB technique to acupuncture point irradiation, attempting to detect its effects by using electrical conductivity measurements. We reviewed relevant literature, searching for information on meridians including their wave-induced flow characteristics.

https://downloads.hindawi.com/journals/ecam/2013/739293.pdf

Wave-Induced Flow in Meridians Demonstrated Using Photoluminescent Bioceramic Material on Acupuncture Points

The high peak-to-average power ratio (PARR) of OFDM signals is a primary disadvantage that single-carrier modulation does not have. Because of using muti-carrier modulation technique, OFDM systems also exhibit a large out-of-band (OOB) emission that can potentially interfere with neighboring transmissions. The precoding scheme using with more null subcarriers achieves significant better PAPR reduction than that using with less subcarriers. But the use of more null subcarriers promotes out-of-band power emission and reduces the transmission rate. The compander, applying Mu (μ)-Law compression and expansion at the transmitter and receiver, is simple and nonlinear method for reducing PAPR. Although the use of nonlinear companding signal has effective reduction in PAPR, it also promotes OOB emission. This paper presents a combination scheme, which using a combination of precoding by utilizing least null subcarriers in frequency domain and nonlinear companding technique by applying proper Mu-Law characteristic in time domain, for reducing PAPR. Simulation results show that the proposed scheme achieves a beneficial trade-off between the reduction of PAPR and OOB power emission in OFDM systems.

PAPR reduction using the combination of precoding and Mu-Law companding techniques for OFDM systems

Suitable scaling schemes are chosen for the Lee's and the Hou's (1984) fast DCT algorithms, and the relative fixed-point roundoff error analyses are carried out, respectively. The average output signal-to-noise ratio are then calculated, and it is shown that in DCT and for N>16 stage-by-stage scaling of Hou's algorithm has the best performance, whereas in inverse DCT, the global scaling of either algorithms has the best performance. >

Comparative performance of fast cosine transform with fixed-point roundoff error analysis

A new fast algorithm is proposed to compute the discrete Hartley transform (DHT) via the Walsh-Hadamard transform (WHT). The processing is carried out on an interframe basis in (N × N) data blocks, where N is an integer power of two. The WHT coefficients are obtained directly, and then used to obtain the DHT coefficients. This is achieved by a transform matrix, the H-transform matrix, which is ortho-normal and has a block-diagonal structure. A complete derivation of the block-diagonal structure for the H-transform matrix is given.

Chau-Yun Hsu

Papers

A study of feature-mapped approach to the multiple travelling salesmen problem

Wave-Induced Flow in Meridians Demonstrated Using Photoluminescent Bioceramic Material on Acupuncture Points

PAPR reduction using the combination of precoding and Mu-Law companding techniques for OFDM systems

Comparative performance of fast cosine transform with fixed-point roundoff error analysis

Fast computation of discrete Hartley transform via Walsh-Hadamard transform