• 한국경영과학회:학술대회논문집
• /
• 한국경영과학회/대한산업공학회 2003년도 춘계공동학술대회
• /
• pp.1056-1064
• /
• 2003

The Euclidean steiner tree problem (ESTP) is to find a minimum-length euclidean interconnection of a set of points in the plane. It is well known that the solution to this problem will be the minimal spanning tree (MST) on some set steiner points, and the ESTP is NP-complete. The ESTP has received a lot of attention in the literature, and heuristic and optimal algorithms have been proposed. In real field, heuristic algorithms for ESTP are popular. A key performance measure of the algorithm for the ESTP is the reduction rate that is achieved by the difference between the objective value of the ESTP and that of the MST without steiner points. In recent survey for ESTP, the best heuristic algorithm showed around $3.14\%$ reduction in the performance measure. We present a evolution programming (EP) for ESTP based upon the Prim algorithm for the MST problem. The computational results show that the EP can generate better results than already known heuristic algorithms.

• 한국컴퓨터정보학회논문지
• /
• 제17권7호
• /
• pp.87-95
• /
• 2012

본 논문에서는 3차원 공간상에 존재하는 많은 입력노드를 신속하게 연결하는 PTAS 3차원 스타이너 최소트리를 제안한다. 스타이너 최소트리문제는 비 다항 적 문제 영역에 속하며 적절한 휴리스틱을 도입했을 경우 다항 적 문제 영역에서 최단 길이의 해를 생성하는 최소신장트리 방법과 같은 여러 방법에 비해 우수한 성능을 보이나, 입력노드의 수가 클 경우 과도한 실행시간을 요구한다. 본 논문에서는 이 문제를 해결하기 위해 PTAS 기법을 도입한 방법을 제안한다. 3차원 공간상에 존재하는 70,000개의 입력 노드에 대한 실험에서, 본 논문에서 제안된 8개 공간 분할 PTAS 방법은, 순수 3차원 스타이너 최소트리방법에 비해 연결 길이는 0.81% 증가했으나, 실행시간은 86.88%의 단축되었다. 이는 제안된 방법이 시간적 제약이 비교적 큰 문제에서 공간상의 많은 노드들을 신속하게 연결하는 응용에 잘 적용될 수 있음을 나타낸다.

• 경영과학
• /
• 제26권1호
• /
• pp.65-76
• /
• 2009

The undirected Steiner tree problem in graphs is known to be NP-hard. The objective of this problem is to find a shortest tree containing a subset of nodes, called terminal nodes. This paper proposes a method based on a two-step procedure to solve this problem efficiently. In the first step. graph reduction rules eliminate useless nodes and edges which do not contribute to make an optimal solution. In the second step, a max-min ant colony optimization combined with Prim's algorithm is developed to solve the reduced problem. The proposed algorithm is tested in the sets of standard test problems. The results show that the algorithm efficiently presents very correct solutions to the benchmark problems.

• Journal of Communications and Networks
• /
• 제9권1호
• /
• pp.84-92
• /
• 2007

This paper deals with the creation of multicast trees in a differentiated services (DiffServ) domain. Initially, we model the integration problems of multicast & DiffServ and give a general de-scription of our framework for multicast provisioning in DiffServ domains. Within this framework, we introduce a novel heuristic algorithm which calculates the multicast trees efficiently. The multicast tree's format and the bandwidth constraints per service class are modeled. The heuristic is based on the Dijkstra's shortest path algorithm and aims to produce the cheapest possible trees (Steiner tree problem) that conform to the defined model. The produced trees can be considered as DiffServ-customized Steiner trees. Furthermore, we evaluate the algorithm with theoretical and experimental analysis and finally, we present our conclusions.

• 한국경영과학회지
• /
• 제25권3호
• /
• pp.17-33
• /
• 2000

We consider the Steiner tree packing problem. For a given undirected graph G =(V, E) with positive integer capacities and non-negative weights on its edges, and a list of node sets(nets), the problem is to find a connection of nets which satisfies the edge capacity limits and minimizes the total weights. We focus on the switchbox routing problem in knock-knee model and formulate this problem as an integer programming using Steiner tree variables. The model contains exponential number of variables, but the problem can be solved using a polynomial time column generation procedure. We test the algorithm on some standard test instances and compare the performances with the results using cutting plane approach. Computational results show that our algorithm is competitive to the cutting plane algorithm presented by Grotschel et al. and can be used to solve practically sized problems.

• Management Science and Financial Engineering
• /
• 제12권2호
• /
• pp.63-69
• /
• 2006

To generate a multicast routing tree guaranteeing the quality of service (QoS), we consider the hop constrained Steiner tree problem and propose a new mathematical formulation for it, which contains fewer constraints than a known formulation. An efficient procedure is also proposed to solve the problem. Preliminary tests show that the procedure reduces the computing time significantly.

• 한국경영과학회:학술대회논문집
• /
• 한국경영과학회 2005년도 추계학술대회 및 정기총회
• /
• pp.27-37
• /
• 2005

The rectilinear Steiner tree problem (RSTP) is to find a minimum-length rectilinear interconnection of a set of terminals in the plane. It is well known that the solution to this problem will be the minimal spanning tree (MST) on some set Steiner points. The RSTP is known to be NP-complete. The RSTP has received a lot of attention in the literature and heuristic and optimal algorithms have been proposed, A key performance measure of the algorithm for the RSTP is the reduction rate that is achieved by the difference between the objective value of the RSTP and that of the MST without Steiner points. A hybrid evolution strategy on RSTP based upon the Prim algorithm was presented. The computational results show that the evolution strategy is better than the previously proposed other heuristic. The average reduction rate of solutions from the evolution strategy is about 11%, which is almost similar to that of optimal solutions.

• 산업경영시스템학회지
• /
• 제23권61호
• /
• pp.33-39
• /
• 2000

In this paper, we present an algorithm for the multicast routing problem when there exit the cell replication limits of ATM switching nodes. This problem can be formulated as a Degree Constrained Minimum Steiner Tree Problem(DCSP). The proposed algorithm is a modification of the shortest path heuristic originally devised for minimum Steiner tree problem. From the experimental results, it can be seen that our algorithm is efficient to obtain a near optimal solution with comparatively low computational time.

• Journal of Information Processing Systems
• /
• 제13권1호
• /
• pp.104-113
• /
• 2017

In this paper, we present an approach to transmit data from the source to the destination through a minimal path (least-cost path) in a computer network of n nodes. The motivation behind our approach is to address the problem of finding a minimal path between the source and destination. From the work we have studied, we found that a Steiner tree with bounded Steiner vertices offers a good solution. A novel algorithm to construct a Steiner tree with vertices and bounded Steiner vertices is proposed in this paper. The algorithm finds a path from each source to each destination at a minimum cost and minimum number of Steiner vertices. We propose both the sequential and parallel versions. We also conducted a comparative study of sequential and parallel versions based on time complexity, which proved that parallel implementation is more efficient than sequential.

• Journal of Communications and Networks
• /
• 제4권3호
• /
• pp.246-255
• /
• 2002

Constrained minimum Steiner tree (CMST) problem is a key issue in multicast routing with quality of service (QoS) support. Bounded shortest path algorithm (BSMA) has been recognized as one of the best algorithms for the CMST problem due to its excellent cost performance. This algorithm starts with a minimumdelay tree, and then iteratively uses a
-shortest-path (KSP) algorithm to search for a better path to replace a “superedge” in the existing tree, and consequently reduces the cost of the tree. The major drawback of BSMA is its high time complexity because of the use of the KSP algorithm. For this reason, we investigate in this paper the possibility of more efficient implementations of BSMA by using different methods to locate the target path for replacing a superedge. Our experimental results indicate that our methods can significantly reduce the time complexity of BSMA without deteriorating the cost performance.