Improving bounds on link failure tolerance of the star graph

In this paper, we present an assessment of the blocking performance of wavelength routed optical networks with chordal ring topology. The performance is focused on chord lengths of 3, N/4, and \(\sqrt N + 3\), being N the number of nodes. It is shown that, in a 100-node chordal ring network, the use of the chord length of N/4 instead of 3 clearly reduces the blocking probability. A reduction of the blocking probability is also observed when the chord length of \(\sqrt N + 3\) is used, instead of N/4 or w=3. The increase of the node degree from 3 (chordal ring with 100 nodes and a chord length of \(\sqrt N + 3\)) to 4 (mesh torus with 100 nodes) has also revealed an important feature: very small blocking gains were observed due to the increase of the node degree from 3 to 4. Thus, the choice of a chordal ring with a chord length of \(\sqrt N + 3\), instead of a mesh-torus, leads to a reduction in the number of network links, and hence in the total cable length, since the number of links in a N-node chordal ring is 3N, and the number of links in a N-node mesh-torus is 4N.

A control-theoretic approach to disseminating values and overcoming malicious links in wireless networks

In this paper we study on-line wavelength assignment in wavelength-routed WDM networks under both unicast and multicast traffic. We assume nodes in the networks have wavelength conversion ability. Since wavelength converters are still expensive and difficult to implement, we consider the networks that have only a limited number of converters in each node, and the converters are shared by all input channels at the node. We consider how to set up connections in such networks using as few wavelength converters as possible. For unicast traffic, we first study the problem of setting up a lightpath on a given link path with minimum number of conversions, and give a new algorithm that solves it in O(tk) time, where t is the number of links on the path and k is the number of wavelengths per fiber, as compared to the best known existing algorithm that runs in at least O(t/sup 2/k) time. We also consider the case when nodes have different conversion priorities, and give an O(tk) time algorithm for setting up a lightpath on a given link path while converting wavelength at higher priority nodes only when necessary. We then generalize this technique to WDM networks with arbitrary topologies and present an algorithm that sets up an optimal lightpath network-wide in O(Nk + Lk) time by checking the state of the entire network, where N and L are the number of nodes and links in the network, respectively. For multicast traffic, finding an optimal multicast light-tree is known to be NP-hard and is usually solved by first finding a link tree then finding a light tree on the link tree. Finding a link tree is also NP-hard and has been extensively studied. Thus, we focus on the second problem which is to set up a light tree on a given link tree with minimum number of conversions. We propose a new and more practical multicast conversion model, where the output of the wavelength converter can be split. As can be seen, the new model can save the usage of converters considerably. We first show that this problem is NP-hard and then give efficient heuristics to solve it approximately.

In this paper, we study on-line wavelength assignment in wavelength-routed WDM networks under both unicast and multicast traffic where nodes in the networks have wavelength conversion ability. Since wavelength converters are still expensive and difficult to implement, we consider the case where nodes in networks have only a limited number of converters that are shared by all input channels. We study the problem of setting up connections in such networks using minimum number of wavelength converters. For unicast traffic, we first study the problem of setting up a lightpath on a given link-path with minimum number of conversions. We give a simple algorithm that solves it in O(tk) time where t is the number of links on the path and k is the number of wavelengths per fiber, as compared to the best known existing method that needs to construct an auxiliary graph and apply the Dijkstra's algorithm. We also consider the problem of setting up a lightpath while using wavelength converters at nodes with fewer available converters only when necessary, and give an O(tk) time algorithm. We then generalize this technique to WDM networks with arbitrary topologies and give an algorithm that sets up an optimal lightpath network-wide in O(Nk+Lk) time, where N and L are the number of nodes and links in the network, respectively. We also consider multicast traffic in this paper. Finding an optimal multicast light-tree is known to be NP-hard and is usually solved by first finding a link-tree then finding a light-tree on the link-tree. Finding an optimal link-tree is also NP-hard and has been extensively studied. Thus, we focus on the second problem which is to set up a light-tree on a given link-tree with minimum number of conversions. We propose a new multicast conversion model with which the output of the wavelength converter is split-table to save the usage of converters. We show that under this model the problem of setting up an optimal light-tree is NP-hard and then give efficient heuristics to solve it approximately

Some topological properties of star graphs: The surface area and volume

Robustness and Optimization of Complex Networks: Reconstructability, Algorithms and Modeling

CHAPTER 7 - Comparisons among Different Interconnection Strategies

Colorectal cancer is a threat to human health, the disease rate of stage Ⅱ colorectal cancer is increasing. Some prognostic factors have been researched, and the number of harvested lymph nodes is a very important factor. Harvesting more lymph nodes will reduce the relapse rate and increase the survival rate. It remains controversial for the minimum number of lymph nodes, and UICC and AJCC recommended that the minimum number was 12. Some factors will influence the number of harvested lymph nodes,for ex-ample, the patient's situation, tumor itself, surgeon and pathologist's skills , and so on. Key words: colorectal tumor; lymph node; prognosis

We derive some properties of the star graph in this paper. In particular, we compute the number of nodes at distance i from a fixed node e in a star graph. To this end, a recursive formula is first obtained. This recursive formula is, in general, hard to solve for a closed form solution. We then study the relations among the number of nodes at distance i to node e in star graphs of different dimensions. This study reveals a very interesting relation among these numbers, which leads to a simple homogeneous linear recursive formula whose characteristic equation is easy to solve. Thus, we get a systematic way to obtain a closed form solution with given initial conditions for any fixed i.

In this paper a fault tolerant routing algorithm on star graph is proposed. Each node in an n-star is associated with a fault-vector of d=\(\lceil \frac{3(n-1)}{2} \rceil\) bits, which is an approximate measure of the number and distribution of faults in the neighborhood. The routing algorithm based on the fault-vector finds the shortest path between any source-destination pair in presence of large number of faulty nodes or links. Simulation results show that the % of cases where the algorithm fails to find a shortest path even when a shortest path exists, is as low as 2.7 with 140 node or link faults in a 7-star.

최근에 병렬처리를 위한 새로운 위상으로 하이퍼 스타 연결망 HS(2n,n)가 제안되었다. 하이퍼 스타 연결망은 하이퍼큐브와 스타 그래프의 성질을 가지고 있으면서, 같은 노드수를 갖는 하이퍼큐브보다 망비용이 우수한 연결망이다. 본 논문에서는 하이퍼스타 연결망 HS(2n,n)에서 에지 중복 없는 스패닝 트리를 구성하는 알고리즘을 제안한다. 그리고 제안한 알고리즘에 의해 구성된 에지 중복 없는 스패닝 트리가 에지 중복없는 최적 스패닝 트리임을 증명한다. Recently, a HyperStar network HS(2n,n) has been introduced as a new interconnection network of new topology for parallel processing. HyperStar network has properties of hypercube and star graph, further improve the network cost of a hypercube with the same number of nodes. In this paper, we show a construction algorithm of edge-disjoint spanning trees in HyperStar network HS(2n,n). Also, we prove that edge-disjoint spanning tree by the algorithm is optimal.

Numerous tourism researchers have studied the information search behaviour of tourists. However, a dearth of scholarship has been devoted to examining tourists’ information search behaviour from a network perspective. This study investigates the significant associations between the networks of contingency factors (i.e. purpose of trip, composition of travel party, and number of visit) and search outcomes (i.e. length of stay and number of attractions visited). Of the raw data collected from international visitors by a metropolitan government in South Korea, this study used the data of visitors who searched their tourism information online. The authors compared the descriptive characteristics of the networks by number of nodes, number of links, and network density scores. The quadric assignment procedure (QAP) correlation analysis reveals positive correlations between the contingency networks and the search outcome networks although it also identified differences in the strength. The theoretical and practical implications contribute to a better understanding of tourism information search behaviour, such as the complex connection patterns between tourism information categories, which the authors discuss in the conclusion.

Reliability polynomials can cross twice

The aim of the research described in this paper has been to construct a model to enable an analysis to be made of the quality of service in both high speed rail (HSR) and air transport (AT) networks and, on this basis, establish conditions for competition between HSR and AT systems. The model is based on the known physical characteristics of both networks, represented by the number of nodes, the number of links, strategies for linking individual nodes; the system characteristics of the two modes of transport—the set of high speed trains and aircraft used (numbers of seats and unit operating costs); the characteristics of the demand between individual nodes on the network in a given interval of time; and the costs of transport in each system. The chief outputs of the model are: total passenger travel costs between origins and destinations, using HSR and AT, and the minimum total costs of the systems. Both types of costs are used as criteria to establish the conditions for competition between high speed raid (HSR) and air transport (AT).

Devising a protocol for computing the location of a sensor in a wireless sensor network (WSN) is a challenging task. In this paper, we present a protocol for computing the location of a sensor that is part of a WSN. The proposed protocol is based on the extent of the trust contained in the reply messages sent by the neighboring sensors that are either anchors or already localized nodes against the request messages sent by the node intending to localize itself. The proposed protocol is distributed, localized, and asynchronous. It does not require any prior knowledge of the topology of the network. The computational and communication complexities of the proposed protocol are O(E) and O(2E + V), respectively, where E is the number of links and V is the number of nodes in the network. The proposed protocol provides a significant improvement in terms of the computational and communication overhead over the existing protocols.