Parallel computations on a graph

Burdonov, Igor; Kossatchev, A. S.; Kulyamin, V. V.

doi:10.1134/s0361768815010028

Cited by 3 publications

(1 citation statement)

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“…Placement of internal sensors has been considered in the engineering and computer science literature, see, e.g. [26,27]. We are unaware of any mathematical works treating the inverse problem on general tree graphs with measurements at the internal vertices, except for [8] where the interior vertices are assumed to satisfy delta-prime matching conditions instead of (3), (4).…”

Section: Figure 3 ω and Subtree ω Kjmentioning

confidence: 99%

An inverse problem for quantum trees with observations at interior vertices

Avdonin¹,

Edward²

2021

NHM

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In this paper we consider a non-standard dynamical inverse problem for the wave equation on a metric tree graph. We assume that positive masses may be attached to the internal vertices of the graph. Another specific feature of our investigation is that we use only one boundary actuator and one boundary sensor, all other observations being internal. Using the Dirichlet-to-Neumann map (acting from one boundary vertex to one boundary and all internal vertices) we recover the topology and geometry of the graph, the coefficients of the equations and the masses at the vertices.

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Section: Figure 3 ω and Subtree ω Kjmentioning

confidence: 99%

An inverse problem for quantum trees with observations at interior vertices

Avdonin¹,

Edward²

2021

NHM

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Building direct and back spanning trees by automata on a graph

Burdonov¹,

Kossachev²

2014

Proceedings of ISP RAS

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The paper presents a parallel graph exploration algorithm. Automaton on a graph is an analogue of the Turing machine-tape cells correspond to graph vertices, where the automaton can store some data, and moves along the tape correspond to moves along graph arcs. This system can be considered also as an aggregate of finite automatons located in graph vertices and interacting by message sending. Each automaton changes its state according to the data stored in the corresponding vertex, and moves along graph arcs are replaced with messages sent by the automaton of the arc's starting vertex to the one of the ending vertex. The suggested parallel graph exploration algorithm has worst case working time bound O(n/k+D), where n is the number of vertices, and D is the graph diameter, the maximum length of simple path (non-self intersecting path). As a result the algorithm builds two spanning trees of the graph: the direct spanning tree, which has the root vertex as its tree root and is directed from the root, and the back spanning tree, directed to the root.

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