• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.129-142
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• 2003

In this paper we study the chromatic sum functions for rooted nonseparable simple maps on the plane. The chromatic sum function equation for such maps is obtained . The enumerating function equation of such maps is derived by the chromatic sum equation of such maps. From the chromatic sum equation of such maps, the enumerating function equation of rooted nonseparable simple bipartite maps on the plane is also derived.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.145-155
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• 2002

In this paper we study the rooted loopless maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating function is obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.7A
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• pp.1080-1089
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• 1999

The union upper bounds to the bit error probability of maximum likelihood(ML) soft-decoding of parallel concatenated convolutional codes(PCCC) and serially concatenated convolutional codes(SCCC) can be evaluated through the weight enumerating function(WEF). This union upper bounds become the lower bounds of the BER achievable when iterative decoding is used. In this paper, to compute the WEF, an efficient error event search algorithm which is a combination of stack algorithm and bidirectional search algorithm is proposed. By computor simulation, it is shown that the union boounds obtained by using the proposed algorithm become the lower bounds to BER of concatenated convolutional codes with iterative decoding.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.537-542
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• 1998

Logic functions such as fuzzy switching functions and multiple-valued Kleenean functions, that are models of Kleene algebra have been studied as foundation of fuzzy logic. This paper deals with a new kinds of functions-fuzzy switching functions with constants-which have features of both the above two kinds of functions . In this paper, we propose new canonical forms for enumerating them. They are much useful to estimate simply the number of fuzzy switching functions with constants.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.621-633
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• 2002

This paper provides some functional equations and parametric expressions of f-essential maps on the projective plane, on the torus and on the Klein bottle with the size as a parameter and gives their explicit formulae for exact enumeration further.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1595-1604
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• 2017

We give a complete formula for the characteristic polynomial of hyperplane arrangements ${\mathcal{J}}_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $1{\leq}i$, j, k, $l{\leq}n$. The formula is obtained by associating hyperplane arrangements with graphs, and then enumerating central graphs via generating functions for the number of bipartite graphs of given order, size and number of connected components.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.329-337
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• 2005

This paper is to establish a functional equation satisfied by the generating function for counting rooted cubic c-nets and then to determine the parametric expressions of the equation directly. Meanwhile, the explicit formulae for counting rooted cubic c-nets are derived immediately by employing Lagrangian inversion with one or two parameters. Both of them are summation-free and in which one is just an answer to the open problem (8.6.5) in [1].

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.329-335
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• 2007

A map is bisingular if each edge is either a loop or an isthmus (i.e., on the boundary of the same face). In this paper we study the number of rooted bisingular maps on the sphere and the torus, and we also present formula for such maps with four parameters: the root-valency, the number of isthmus, the number of planar loops and the number of essential loops.

• Proceedings of the KOR-KST Conference
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• 2000.02a
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• pp.25-47
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• 2000

In route guidance systems fastest-path routing has typically been adopted because of its simplicity. However, empirical studies on route choice behavior have shown that drivers use numerous criteria in choosing a route. The objective of this study is to develop computationally efficient algorithms for identifying a manageable subset of the nondominated (i.e. Pareto optimal) paths for real-time vehicle routing which reflect the drivers' preferences and route choice behaviors. We propose two pruning algorithms that reduce the search area based on a context-dependent linear utility function and thus reduce the computation time. The basic notion of the proposed approach is that ⅰ) enumerating all nondominated paths is computationally too expensive, ⅱ) obtaining a stable mathematical representation of the drivers' utility function is theoretically difficult and impractical, and ⅲ) obtaining optimal path given a nonlinear utility function is a NP-hard problem. Consequently, a heuristic two-stage strategy which identifies multiple routes and then select the near-optimal path may be effective and practical. As the first stage, we utilize the relaxation based pruning technique based on an entropy model to recognize and discard most of the nondominated paths that do not reflect the drivers' preference and/or the context-dependency of the preference. In addition, to make sure that paths identified are dissimilar in terms of links used, the number of shared links between routes is limited. We test the proposed algorithms in a large real-life traffic network and show that the algorithms reduce CPU time significantly compared with conventional multi-criteria shortest path algorithms while the attributes of the routes identified reflect drivers' preferences and generic route choice behaviors well.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.18 no.35
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• pp.47-52
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• 1995

The aim of this paper is to suggest the cutting stock problems which are two-dimensional in form, but can be treated as the optimization methods for one-dimensional cutting stock problem by exploiting the length requirement of the products. The solution method consists of two stages. The first calculates the number of roll pieces of each size. Next, 1-dimensional cutting stock model is set up. One heuristic method to calculate the number of each roll is suggested. The trim loss minization criteria are used to design the objective function. This model can be solved by the conventional cutting stock procedures based on enumerating the possible cutting patterns.