# Sensor Location Problem for a Multigraph

Pilipchuk, L. A.; Vishnevetskaya, T. S.; Pesheva, Y. H.

Mathematica Balkanica New Series (2013)

- Volume: 27, Issue: 1-2, page 65-75
- ISSN: 0205-3217

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topPilipchuk, L. A., Vishnevetskaya, T. S., and Pesheva, Y. H.. "Sensor Location Problem for a Multigraph." Mathematica Balkanica New Series 27.1-2 (2013): 65-75. <http://eudml.org/doc/281411>.

@article{Pilipchuk2013,

abstract = {MSC 2010: 05C50, 15A03, 15A06, 65K05, 90C08, 90C35We introduce sparse linear underdetermined systems with embedded network structure. Their structure is inherited from the non-homogeneous network ow programming problems with nodes of variable intensities. One of the new applications of the researched underdetermined systems is the sensor location problem (SLP) for a multigraph. That is the location of the minimum number of sensors in the nodes of the multigraph, in order to determine the arcs ow volume and variable intensities of nodes for the whole multigraph. Research of the rank of the sparse matrix is based on the constructive theory of decomposition of sparse linear systems.},

author = {Pilipchuk, L. A., Vishnevetskaya, T. S., Pesheva, Y. H.},

journal = {Mathematica Balkanica New Series},

keywords = {Sparse linear system; underdetermined system; basis of the solution space of a homogeneous sparse linear system; network support; decomposition of a support; forest of trees; characteristic vector; variable intensity; sensor location problem; sparse linear system},

language = {eng},

number = {1-2},

pages = {65-75},

publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},

title = {Sensor Location Problem for a Multigraph},

url = {http://eudml.org/doc/281411},

volume = {27},

year = {2013},

}

TY - JOUR

AU - Pilipchuk, L. A.

AU - Vishnevetskaya, T. S.

AU - Pesheva, Y. H.

TI - Sensor Location Problem for a Multigraph

JO - Mathematica Balkanica New Series

PY - 2013

PB - Bulgarian Academy of Sciences - National Committee for Mathematics

VL - 27

IS - 1-2

SP - 65

EP - 75

AB - MSC 2010: 05C50, 15A03, 15A06, 65K05, 90C08, 90C35We introduce sparse linear underdetermined systems with embedded network structure. Their structure is inherited from the non-homogeneous network ow programming problems with nodes of variable intensities. One of the new applications of the researched underdetermined systems is the sensor location problem (SLP) for a multigraph. That is the location of the minimum number of sensors in the nodes of the multigraph, in order to determine the arcs ow volume and variable intensities of nodes for the whole multigraph. Research of the rank of the sparse matrix is based on the constructive theory of decomposition of sparse linear systems.

LA - eng

KW - Sparse linear system; underdetermined system; basis of the solution space of a homogeneous sparse linear system; network support; decomposition of a support; forest of trees; characteristic vector; variable intensity; sensor location problem; sparse linear system

UR - http://eudml.org/doc/281411

ER -

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