Augmenting Forests to Meet Odd Diameter Requirements

Ishii, Toshimasa; Yamamoto, Shigeyuki; Nagamochi, Hiroshi

doi:10.1007/978-3-540-24587-2_45

Cited by 13 publications

(12 citation statements)

References 14 publications

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“…[2], [3], [4] deal with the problems for determining a set of edges to meet a required edgeconnectivity or vertex-connectivity by adding edges to a graph. [5], [6], [7] deal with the problems for determining a set of edges to meet a required diameter by adding edges to a graph. There are the Chordal graph completion problem, the Interval graph completion problem, and the Hamilton graph completion problem that determine a set of added edges to make a given graph a Chordal graph, an Interval graph, and a Hamilton graph, respectively [5].…”

Section: Related Workmentioning

confidence: 99%

Detecting protected links to keep reachability to server against failures

Imagawa

Miwa

2013

The International Conference on Information Networking 2013 (ICOIN)

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Methods to design a reliable network against network failures are important for Internet service providers (ISPs). ISPs must offer connectivity to users, even if link failures occur. The best way to design a reliable network is to protect all links so that the failure probability of a link is sufficiently small by sufficient backup resource and rapid recovery system. However, sufficient backup resource needs much cost for ISP. Therefore, it is necessary to find the smallest number of links to be protected such that, even if any non-protected links fail, the resulting network offers users connectivity. In this paper, as a measure of connectivity, we focus on the size of the connected component including a server or a gateway. Critical links whose failures drastically decrease the size of the connected component including a server must be protected not to fail, because such a failure prevent a large number of users from access to the server. Similarly, when a server is a gateway to another ISP's network, many users cannot communicate with exterior users and servers. Our purpose is to find the links to be protected such that, even if any non-protected links fail, the number of the nodes connected with a server in the resulting network is not less than a threshold.In this paper, we formulate this problem and prove that the problem is NP-hard. In addition, we propose a polynomialtime algorithm to solve the problem that the number of the simultaneous link failures is restricted to one. Furthermore, we present a polynomial-time algorithm to solve the problem that the number of the simultaneous link failures is restricted to two and a network is a tree.

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Section: Related Workmentioning

confidence: 99%

Detecting protected links to keep reachability to server against failures

Imagawa

Miwa

2013

The International Conference on Information Networking 2013 (ICOIN)

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“…Here diameter is the distance between two nodes which are farthest from each other where distance is the shortest path length connecting two nodes. The problem can be solved in polynomial time if a graph is a tree [7] else is a NP-Complete problem [8]. [9] Determine the set of edge to be added on given graph in order to construct completion problem graph like chordal graph, Hamilton graph and interval graph.…”

Section: Related Workmentioning

confidence: 99%

Stable match approach to determine vital link to preserve shortest path length

Gupta

Nitin

2015

International Conference on Computing, Communication &Amp; Automation

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Content Delivery Network is a large distributed system consisting of multiple servers deployed in much geographical location that delivers the content to end user with high performance and high availability. But the increase load of content delivery server and network degrades the quality of service. Also 70% of unintentional failures are Single link failure which creates potential failure along the delivery chains. To get over the problem some mirror server are placed in the network where a request is transferred to one of the mirror servers such that connectivity between user and server is within small hop count even during the failure. This paper targets the stability of network reliability by providing hop length stability and network connectivity.We use the stable matching approach on the network to find the vital link to be protected so that user can access the server within small hop count even if non -vital links fails. Moreover, we prove that the problem can solved in polynomial time conditioned when hop count is determined to be one.

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“…[4], [5], [6] address the problems for determining a set of edges to meet a required edge-connectivity or vertexconnectivity by adding edges to a graph. Considering path length, [7], [8], [9] address the problems for determining a set of edges to meet a required diameter by adding edges to a graph. Chordal Graph Completion Problem, Interval Graph Completion Problem, and Hamilton Graph Completion Problem determine a set of added edges to make a given graph a chordal graph, an interval graph, and a Hamilton graph, respectively [7].…”

Section: Related Workmentioning

confidence: 99%

Network Design Method by Link Protection for Network Load Alleviation against Failures

Noguchi

Fujimura

Miwa

2011

2011 Third International Conference on Intelligent Networking and Collaborative Systems

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Network reliability is needed as the Internet becomes an important social infrastructure. However, we face risks of failure and congestion on many links or routers; therefore, a network should be robust enough to avoid failure and congestion. As the route of a path between two nodes is automatically determined by a routing protocol, many paths may be included in a same link and it may cause congestion. Especially, when a link fails, the routes of the paths included in the link are automatically changed, and eventually congestion may occur. If there are critical links whose failures cause congestion, they must be protected by the function that a failed link is rapidly switched to its backup link in the lower layer and the failure is not detected over the IP layer. However, such a link protection increases investment cost for facilities and operational cost. In this paper, we formulate the problem to find links to be protected so that no congestion occurs even if any non-protected links fails. We prove that this problem is NP-hard. In addition, we present a polynomial-time algorithm to solve the problem that the number of simultaneously failed links is restricted to one.

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Augmenting Forests to Meet Odd Diameter Requirements

Cited by 13 publications

References 14 publications

Detecting protected links to keep reachability to server against failures

Detecting protected links to keep reachability to server against failures

Stable match approach to determine vital link to preserve shortest path length

Network Design Method by Link Protection for Network Load Alleviation against Failures

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