• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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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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• v.9 no.2
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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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• v.13 no.1
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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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• v.4 no.5
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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.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.5_6
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• pp.176-186
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• 2007

An interconnection network can be represented as a graph where a vertex corresponds to a node and an edge corresponds to a link. The diameter of an interconnection network is the maximum length of the shortest paths between all pairs of vertices. The fault diameter of an interconnection network G is the maximum length of the shortest paths between all two fault-free vertices when there are $_k(G)-1$ or less faulty vertices, where $_k(G)$ is the connectivity of G. The fault diameter of an R-regular graph G with diameter of 3 or more and connectivity ${\tau}$ is at least diam(G)+1 where diam(G) is the diameter of G. We show that the fault diameter of a 2-dimensional $m{\times}n$ torus with $m,n{\geq}3$ is max(m,n) if m=3 or n=3; otherwise, the fault diameter is equal to its diameter plus 1. We also show that in $d({\geq}3)$-dimensional $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ torus with each $k_i{\geq}3$, there are 2d mutually disjoint paths joining any two vertices such that the lengths of all these paths are at most diameter+1. The paths joining two vertices u and v are called to be mutually disjoint if the common vertices on these paths are u and v. Using these mutually disjoint paths, we show that the fault diameter of $d({\geq}3)$-dimensional $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ totus with each $k_i{\geq}3$ is equal to its diameter plus 1.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.1B
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• pp.71-79
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• 2003

As the traffic grows rapidly in the Internet, the QoS guarantee of the flows and the traffic engineering problems have become very important issues. MPLS has more advantages to solve the problems than existing IP routing because of its use of multiple paths between the source and destination pairs Particularly, the availability of Constraint-based Shortest Path First(CSPF) algorithm and explicit route in MPLS made the problem referred above to be solved efficiently. However, the CSPF algorithm has the characteristic of selecting the shortest path of all paths which meet the traffics' QoS constraints Therefore, even though there are alternative paths to route traffic, alternate QoS paths may not be found and best-effort traffic will be dropped during congestion period In this paper, we present the network resource optimization method related to the traffic engineering by using load balancing through routing in MPLS network.

• Management Science and Financial Engineering
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• v.12 no.2
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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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• 2004.08a
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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.

• Journal of KIISE:Information Networking
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• v.34 no.2
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• pp.120-133
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• 2007

A multicast tree includes several, possibly a large number of, paths connecting source-receiver pairs, and network failure may disable part of the multicast tree. Reconstruction of the entire multicast tree to recover from a component failure is highly undesirable, because some group members have to suffer service disruptions even though the communication paths to/from them are not affected by the failure. To limit reconfiguration region and to maximize the likelihood of successful reconfiguration, we propose and evaluate a pre-planned reconfiguration policy for QoS multicast sessions. Specifically, we equip a reconfiguration path (RP) with each end-to-end path that connects a source-receiver pair in the multicast tree, and reserve resources in advance along the RPs. Efficient resource-sharing techniques are applied to reduce the amount of resources reserved for RPs but not used in the absence of failures. This way, we prevent uncontrolled competition among different multicast sessions which may simultaneously try to recover from failures. We evaluate the performance of the proposed scheme using simulation on randomly-generated networks. We use the shortest-path routing for QoS multicast sessions, and simulate both source-based and shared multicast trees. The evaluation results indicates that successful pre-planned reconfiguration can be achieved for all group members with reasonable overhead. Our scheme is also shown to adapt well to dynamic changes of group membership.