Graphs: Theory and Algorithms

Thulasiraman, K.; Swamy, M.N.S.

doi:10.1002/9781118033104

Cited by 387 publications

(272 citation statements)

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“…Otherwise G is an undirected or a non oriented graph. In addition, a graph is a simple graph if it has no self-loops or multiedges [17,29]. The digraph G = (V, E) is depicted in Fig.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…(23) represents the number of edges of a complete graph of n t nodes. Equation (24) represents the number of edges in a complete bipartite graph of n t nodes in V 1 and n DC S nodes in V 2 , [29]. Once the DC subsystem is computed considering all possible connections, the invariant part of RPSS (links and AC subsystems) is added.…”

Section: Solution To System Topology Variabilitymentioning

confidence: 99%

“…It must be noticed that the case where all trains are running between two DC nodes can exist. To cover all possibilities, this graph is a complete type graph; that is, a simple one in which every pair of distinct nodes are connected by a unique edge [29].…”

Section: Solution To System Topology Variabilitymentioning

confidence: 99%

“…For a graph G with n nodes (graph order) the matrix with dimension (n, n) that relates the connections between nodes is formed as follows [17,29]:…”

Section: Theoretical Backgroundmentioning

confidence: 99%

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On the Use of Graph Theory for Railway Power Supply Systems Characterization

2015

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Over the years, graph theory has proven to be a key tool in power systems modeling and analysis. In this paper, the authors propose a systematic method for railway power supply systems (RPSS) description that can be applied to any AC/DC system. This method represents the different elements of the RPSS with a set of subgraphs. Merging these subgraphs, the representative graph of the whole RPSS and its associated adjacency and incidence matrices will be obtained. Once these matrices are obtained, Kirchhoff's laws can be easily implemented. In this work, the method is applied to a DC light traction system. The AC system that feeds the traction network through power transformers combined with rectifiers is also included. With the proposed approach, the variability problems in the system topology and dimensions are overcome, obtaining an invariant system, even when the trains change their relative position, or when a new train enters into or exits the system.

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“…Otherwise G is an undirected or a non oriented graph. In addition, a graph is a simple graph if it has no self-loops or multiedges [17,29]. The digraph G = (V, E) is depicted in Fig.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Solution To System Topology Variabilitymentioning

confidence: 99%

Section: Solution To System Topology Variabilitymentioning

confidence: 99%

“…For a graph G with n nodes (graph order) the matrix with dimension (n, n) that relates the connections between nodes is formed as follows [17,29]:…”

Section: Theoretical Backgroundmentioning

confidence: 99%

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On the Use of Graph Theory for Railway Power Supply Systems Characterization

2015

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“…We will use to denote the directed edge from vertex to vertex . We assume standard graph theoretic notations [24], [28], unless specified otherwise.…”

Section: Fast Recovery Using Redundant Treesmentioning

confidence: 99%

Quality-of-service and quality-of-protection issues in preplanned recovery schemes using redundant trees

Xue

Chen

Thulasiraman

2003

IEEE J. Select. Areas Commun.

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Abstract-In this paper, we study quality-of-service (QoS) and quality-of-protection (QoP) issues in redundant tree based preplanned recovery schemes for a single-link failure in two-edge connected graphs and for a single-node failure in two-connected graphs. We present schemes (to be called G-MFBG schemes) that generalize the schemes (to be called MFBG schemes) developed by Médard et al. to construct a pair of redundant trees, called red and blue trees, which guarantees fast recovery from any single-link/node failure, as long as the failed node is not the root node. Using the G-MFBG schemes, we study QoS issues relating to red/blue trees. We present effective heuristics for computing a pair of redundant trees with low average delay or small total cost. We develop an optimal algorithm for computing a pair of red/blue trees with maximum bandwidth. Furthermore, a pair of red/blue trees guarantees fast recovery from simultaneous multiple failures if it satisfies certain properties. This leads us to define the concept of QoP of a pair of red/blue trees. We present an effective heuristic to construct a pair of red/blue trees with high QoP. The paper concludes with a discussion of computational results that demonstrate the effectiveness of the different algorithms presented.

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