• Journal of the Institute of Electronics Engineers of Korea TC
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• v.44 no.8
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• pp.62-67
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• 2007

In some wireless sensor networks, the sensor nodes are required to be located sparsely at designated positions over a wide area, introducing the problem of adding minimum number of relay nodes to interconnect the sensor nodes. The problem finds its form in literature: the Minimum number of Steiner Points. Since it is known to be NP-hard, this paper proposes an approximation scheme to estimate the minimum number of relay nodes through the properties of the abstract from. Reducing the number of nodes in a sensor network, the amount of data exchange over the net will be far decreased.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.48 no.2
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• pp.6-13
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• 2011

This paper deals with the interconnection problem in ad-hoc networks or sensor networks, where relay nodes are deployed additionally to form connections between given nodes. This problem can be reduced to a NP-hard problem. The nodes of the networks, by applications or geographic factors, can be deployed densely in some areas while sparsely in others. For such a case one can make an approximation scheme, which gives shorter execution time, for the additional node deployments by ignoring the interconnections inside the dense area of nodes. However, the case is still a NP-hard, so it is proper to establish a polynomial time approximation scheme (PTAS) by implementing a dynamic programming. The analysis can be made possible by an elaboration on making the definition of the objective function. The objective function should be defined to be able to deal with the requirement incurred by the substitution of the dense area with its abstraction.

• Proceedings of the Korean Information Science Society Conference
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• 2006.10a
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• pp.494-499
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• 2006

Given a set S of n points in the plane, a minimum-dilation spanning tree of S is a tree with vertex set S of smallest possible dilation. We show that given a set S of n points and a dilation $\delta$ > 1, it is NP-hard to determine whether a spanning tree of S with dilation at most $\delta$ exists.

• Proceedings of the Korean Information Science Society Conference
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• 2003.10a
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• pp.505-507
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• 2003

SAT 문제는 하드웨어/소프트웨어 검증과 모델 체킹 등 다양한 분야에서 유용하게 사용되고 있으나 복잡도가 NP-complete 라는 어려움을 가지고 있다. 다양한 알고리즘과 휴리스틱, 도구들이 개발되었지만 그럼에도 불구하고 해결할 수 없는 hard instance 들이 존재한다. 이 논문에서는 그러한 hard instance를 해결하기 위한 방법의 하나로 model accumulation을 제안한다.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.284-287
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• 2006

We consider the transportation problem of optimizing the use of trailers and tractors. Several variants with fixed loading and unloading time are discussed. We show that the variant requiring on-time delivery can be solved in polynomial time, whereas the other variant requiring time-window delivery is NP-hard. We also discuss that if the number of loading and unloading operations assigned to each trailer or tractor is limited, even the variant requiring on-time delivery becomes NP-hard.

• Management Science and Financial Engineering
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• v.14 no.1
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• pp.87-90
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• 2008

We show that when a max-cut problem is allowed native-weight edges, to decide if the problem has a cut of a positive weight is NP-hard. This implies that there is no polynomial time algorithm which guarantees a cut whose objective value is no less than $1/p(<I>)$ times the optimum for any polynomially computable polynomial p, where denotes the encoding length of an instance I.