• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.1-23
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• 2005

The shortest-paths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one vertex to another often gives the best way to route a message between the vertices. This paper presents an $O(n^2)$ time sequential algorithm and an $O(n^2/p+logn)$ time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circular-arc graphs, where p and n represent respectively the number of processors and the number of vertices of the circular-arc graph.

• Journal of Multimedia Information System
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• 제9권2호
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• pp.121-126
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• 2022

The shortest path betweenness value of a node quantifies the amount of information passing through the node when all the pairs of nodes in the network exchange information in full capacity measured by the number of the shortest paths between the pairs assuming that the information travels in the shortest paths. It is calculated as the cumulative of the fractions of the number of shortest paths between the node pairs over how many of them actually pass through the node of interest. It's possible for a node to have zero or underrated betweenness value while sitting just next to the giant flow of information. These nodes may have a significant influence on the network when the normal flow of information is disrupted. We propose a betweenness centrality measure called collective betweenness that takes into account the surroundings of a node. We will compare our measure with other centrality metrics and show some applications of it.

• Management Science and Financial Engineering
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• 제13권1호
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• pp.121-126
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• 2007

Among many graphs, directed acyclic graph(DAG) attracts many researchers due to its nice property of existence of topological sort. In some classic graph problems, it is known that, if we use the aforementioned property, then much efficient algorithms can be generated. So, in this paper, new algorithm for the all-pairs shortest path problem in a DAG is proposed. While the algorithm performing the iteration, it identifies the set of essential arcs which requires in a shortest path. So, the proposed algorithm has a running time of $O(m^*n+m)$, where m, n and $m^*$ denote the number of arcs, number of node, and the number of essential arcs in a DAG, respectively.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제4권5호
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• pp.939-955
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• 2010

With the progress of IT and mobile positioning technologies, various types of location-based services (LBS) have been proposed and implemented. Finding a shortest path between two nodes is one of the most fundamental tasks in many LBS related applications. So far, there have been many research efforts on the shortest path finding problem. For instance, $A^*$ algorithm estimates neighboring nodes using a heuristic function and selects minimum cost node as the closest one to the destination. Pruning method, which is known to outperform the A* algorithm, improves its routing performance by avoiding unnecessary exploration in the search space. For pruning, shortest paths for all node pairs in a map need to be pre-computed, from which a shortest path container is generated for each edge. The container for an edge consists of all the destination nodes whose shortest path passes through the edge and possibly some unnecessary nodes. These containers are used during routing to prune unnecessary node visits. However, this method shows poor performance as the number of unnecessary nodes included in the container increases. In this paper, we focus on this problem and propose a new border line-based pruning scheme for path routing which can reduce the number of unnecessary node visits significantly. Through extensive experiments on randomly-generated, various complexity of maps, we empirically find out optimal number of border lines for clipping containers and compare its performance with other methods.

• 한국정보과학회논문지:시스템및이론
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• 제34권5_6호
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• pp.176-186
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• 2007

상호연결망은 그래프로 모델링 할 수 있다: 노드는 정점으로 대응시키고, 링크는 에지로 대응시킨다. 상호연결망(그래프)의 지름은 서로 다른 모든 두 정점 사이의 최단경로 길이 중 최대이다. 상호연결망의 고장지름이란 연결도-1 개 이하의 임의의 정점에 고장이 있을 경우, 이들 고장 정점들을 제거한 연결망에서 모든 두 정점사이의 최단경로 길이 중 최대이다. 지름이 3이상이고 연결도가 r인 r-정규(regular) 그래프의 고장지름은 지름+1이상이다. 이 논문에서는 $m,n{\geq}3$ 인 2-차원 $m{\times}n$ 토러스에서 m=3 혹은 n=3일 때 고장지름은 max(m,n)이고, m,n>3일 때 고장지름은 지름 +1임을 보인다. 그리고 $k_i{\geq}3(1{\leq}i{\leq}d)$이고 $d{\geq}3$인 d- 차원 $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ 토러스에서 서로 다른 임의의 두 정점 사이에 길이가 지름+1이하인 서로소인 경로들이 2d 개 존재함을 보인다. 두 정점 u와 v 사이의 서로소인 경로들이란, 공통의 정점들이 u와 v만 있는 경로들을 말한다. 이들 서로소인 경로들을 이용하여 $k_i{\geq}3(1{\leq}i{\leq}d)$이고 $d{\geq}3$인 d-차원 $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ 토러스의 고장지름이 지름+1임을 보인다.

• 한국통신학회논문지
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• 제28권1B호
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• pp.71-79
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• 2003

인터넷에서 트래픽의 폭발적인 증가로 인하여 데이터 흐름에 대한 서비스품질(QoS) 보장과 트래픽 엔지니어링 문제가 매우 중요하게 되었다 MPLS는 출발지와 목적지 사이에 다중의 경로를 사용하는 데 자유롭기 때문에 기존의 IP 라우팅보다 이러한 문제를 해결하는데 장점을 갖고 있다 특히 제한기반 최소 거리(CSPF) 알고리즘과 MPLS의 explicit 결로는 위의 문제를 해결하도록 해주었다. 그러나, CSPF 알고리즘은 QoS 제한 이내의 최소 거리 경로를 찾기 때문에 QoS가 만족되는 다른 경로를 찾을 수 없으며, 트래픽이 몰리는 정체가 발생하였을 경우 최선형(best-effort) 트래픽 데이터는 잃게 된다. 본 논문에서는 MPLS 망에서 트래픽을 분산시키는 라우팅을 통해 네트워크 자원을 최적으로 사용하는 방안을 제시한다

• Management Science and Financial Engineering
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• 제12권2호
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• pp.87-110
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• 2006

In a hierarchical road network, all roads can be classified according to their attributes such as speed limit, number of lanes, etc. By splitting the whole road network into the subnetworks of the highlevel and low-level roads, we can reduce the size of the network to be calculated at once, and find a path in the way that drivers usually adopt when searching out a travel route. To exploit the hierarchical property of road networks, we define a convenient path and propose an algorithm for finding convenient paths. We introduce a parameter indicating the driver's tolerance to the difference between the length of a convenient path and that of a shortest convenient path. From this parameter, we can determine how far we have to search for the entering and exiting gateway. We also propose some techniques for reducing the number of pairs of entries and exits to be searched in a road network. A result of the computational experiment on a real road network is given to show the efficiency of the proposed algorithm.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.772-776
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• 2004

This paper proposes an interference avoidance approach for Constraint-Based Routing (CBR) algorithm in the Multi-Protocol Label Switching (MPLS) network. The MPLS network itself has a capability of integrating among any layer-3 protocols and any layer-2 protocols of the OSI model. It is based on the label switching technology, which is fast and flexible switching technique using pre-defined Label Switching Paths (LSPs). The MPLS network is a solution for the Traffic Engineering(TE), Quality of Service (QoS), Virtual Private Network (VPN), and Constraint-Based Routing (CBR) issues. According to the MPLS CBR, routing performance requirements are capability for on-line routing, high network throughput, high network utilization, high network scalability, fast rerouting performance, low percentage of call-setup request blocking, and low calculation complexity. There are many previously proposed algorithms such as minimum hop (MH) algorithm, widest shortest path (WSP) algorithm, and minimum interference routing algorithm (MIRA). The MIRA algorithm is currently seemed to be the best solution for the MPLS routing problem in case of selecting a path with minimum interference level. It achieves lower call-setup request blocking, lower interference level, higher network utilization and higher network throughput. However, it suffers from routing calculation complexity which makes it difficult to real task implementation. In this paper, there are three objectives for routing algorithm design, which are minimizing interference levels with other source-destination node pairs, minimizing resource usage by selecting a minimum hop path first, and reducing calculation complexity. The proposed CBR algorithm is based on power factor calculation of total amount of possible path per link and the residual bandwidth in the network. A path with high power factor should be considered as minimum interference path and should be selected for path setup. With the proposed algorithm, all of the three objectives are attained and the approach of selection of a high power factor path could minimize interference level among all source-destination node pairs. The approach of selection of a shortest path from many equal power factor paths approach could minimize the usage of network resource. Then the network has higher resource reservation for future call-setup request. Moreover, the calculation of possible path per link (or interference level indicator) is run only whenever the network topology has been changed. Hence, this approach could reduce routing calculation complexity. The simulation results show that the proposed algorithm has good performance over high network utilization, low call-setup blocking percentage and low routing computation complexity.

• 한국정보과학회논문지:정보통신
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• 제34권2호
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• pp.120-133
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• 2007

전송-수신 쌍들을 연결하는 많은 수의 경로들로 이루어진 멀티캐스트 트리에서 네트워크 구성요소의 실패는 멀티캐스트 트리의 일부를 손상시킬 수 있다. 그러나 하나의 구성요소의 실패를 복구하기 위해 전체 멀티캐스트 트리를 다시 만드는 것은, 실패의 영향을 받지 않은 경로를 사용하는 그룹 멤버들까지도 서비스의 중단을 겪어야 하기 때문에 바람직하지 않다. 본 논문은 QoS 멀티캐스트 트리에서 재구성해야 할 영역을 줄이면서 재구성의 성공 가능성을 최대화하는 계획된 재구성(Pre-Planned Reconfiguration: PPR) 정책을 제안한다. PPR 방식은 멀티캐스트 트리의 전송-수신 쌍을 연결하는 각 경로에 재구성 경로를 미리 만들고, 이들 경로에 필요한 자원을 미리 예약해 둔다. 이를 위해 우리는 기존 멀티캐스트 트리의 변화를 최소화하며 손상되지 않은 부분들의 서비스를 최대한 유지하는 재구성 경로의 라우팅 방법을 고안하였으며, 효율적 자원 공유 방법을 사용하여 재구성 경로들을 위해 예약된(실패가 일어나지 않을 경우 사용되지 않는) 자원의 양을 줄인다. PPR 방식은 실패 복구를 위해 여러 멀티캐스트 세션들이 동시에 엄청난 경쟁을 하는 것을 막을 수 있다. 시물레이션을 통해 최단경로 라우팅을 사용하는 전송자 중심 멀티캐스트 트리와 공유 멀티 캐스트 트리에서 각각 성능을 평가한 결과 PPR 방식은 적당한 오버헤드내에서 모든 그룹 멤버들에게 성공적인 재구성을 제공한다. 또한 PPR 방식은 그룹 멤버쉽이 동적으로 변화할 때에도 잘 적응한다.