Assigning sensors to missions with demands

Amotz Bar-Noy, Theodore Brown, Matthew P. Johnson, Thomas La Porta, Ou Liu, Hosam Rowaihy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

Abstract

We introduce Semi-Matching with Demands (SMD), which models a certain problem in sensor networks of assigning individual sensors to sensing tasks. If there are multiple sensing tasks or missions to be accomplished simultaneously, and if sensor assignment must be exclusive, then this is a bipartite semi-matching problem. Each mission is associated with a demand value and a profit value; each sensor-mission pair is associated with a utility offer (possibly 0). The goal is a sensor assignment that maximizes the profits of the satisfied missions (with no credit for partially satisfied missions). SMD is NP-hard and as hard to approximate as Maximum Independent Set. Therefore we investigate less difficult constrained versions of the problem. We give a simple greedy Δ-approximation algorithm for a degree-constrained version (Δ-SMD), in which each mission receives positive utility offers from at most Δ sensors. For small Δ, we show that Δ-SMD is equivalent to k-Set Packing (with k = Δ), which yields a polynomial-time (Δ+1)/2-approximation. For Δ=∈2, we solve the problem optimally by reduction to maximum matching. Finally, we introduce a geometric version which remains strongly NP-hard but has a PTAS.

Original languageEnglish (US)
Title of host publicationAlgorithmic Aspects of Wireless Sensor Networks - Third International Workshop, ALGOSENSORS 2007, Revised Selected Papers
Pages114-125
Number of pages12
DOIs
StatePublished - Aug 27 2008
Event3rd International Workshop on Algorithmic Aspects of Wireless Sensor Networks, ALGOSENSORS 2007 - Wroclaw, Poland
Duration: Jul 14 2007Jul 14 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4837 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other3rd International Workshop on Algorithmic Aspects of Wireless Sensor Networks, ALGOSENSORS 2007
CountryPoland
CityWroclaw
Period7/14/077/14/07

Fingerprint

Sensor
Sensors
Profit
Profitability
Sensing
Assignment
NP-complete problem
Set Packing
Maximum Independent Set
Maximum Matching
Approximation algorithms
Matching Problem
Greedy Algorithm
Sensor networks
Sensor Networks
Approximation Algorithms
Polynomial time
Maximise
Polynomials
Approximation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Bar-Noy, A., Brown, T., Johnson, M. P., La Porta, T., Liu, O., & Rowaihy, H. (2008). Assigning sensors to missions with demands. In Algorithmic Aspects of Wireless Sensor Networks - Third International Workshop, ALGOSENSORS 2007, Revised Selected Papers (pp. 114-125). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4837 LNCS). https://doi.org/10.1007/978-3-540-77871-4_11
Bar-Noy, Amotz ; Brown, Theodore ; Johnson, Matthew P. ; La Porta, Thomas ; Liu, Ou ; Rowaihy, Hosam. / Assigning sensors to missions with demands. Algorithmic Aspects of Wireless Sensor Networks - Third International Workshop, ALGOSENSORS 2007, Revised Selected Papers. 2008. pp. 114-125 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Bar-Noy, A, Brown, T, Johnson, MP, La Porta, T, Liu, O & Rowaihy, H 2008, Assigning sensors to missions with demands. in Algorithmic Aspects of Wireless Sensor Networks - Third International Workshop, ALGOSENSORS 2007, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4837 LNCS, pp. 114-125, 3rd International Workshop on Algorithmic Aspects of Wireless Sensor Networks, ALGOSENSORS 2007, Wroclaw, Poland, 7/14/07. https://doi.org/10.1007/978-3-540-77871-4_11

Assigning sensors to missions with demands. / Bar-Noy, Amotz; Brown, Theodore; Johnson, Matthew P.; La Porta, Thomas; Liu, Ou; Rowaihy, Hosam.

Algorithmic Aspects of Wireless Sensor Networks - Third International Workshop, ALGOSENSORS 2007, Revised Selected Papers. 2008. p. 114-125 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4837 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - We introduce Semi-Matching with Demands (SMD), which models a certain problem in sensor networks of assigning individual sensors to sensing tasks. If there are multiple sensing tasks or missions to be accomplished simultaneously, and if sensor assignment must be exclusive, then this is a bipartite semi-matching problem. Each mission is associated with a demand value and a profit value; each sensor-mission pair is associated with a utility offer (possibly 0). The goal is a sensor assignment that maximizes the profits of the satisfied missions (with no credit for partially satisfied missions). SMD is NP-hard and as hard to approximate as Maximum Independent Set. Therefore we investigate less difficult constrained versions of the problem. We give a simple greedy Δ-approximation algorithm for a degree-constrained version (Δ-SMD), in which each mission receives positive utility offers from at most Δ sensors. For small Δ, we show that Δ-SMD is equivalent to k-Set Packing (with k = Δ), which yields a polynomial-time (Δ+1)/2-approximation. For Δ=∈2, we solve the problem optimally by reduction to maximum matching. Finally, we introduce a geometric version which remains strongly NP-hard but has a PTAS.

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SN - 9783540778707

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Bar-Noy A, Brown T, Johnson MP, La Porta T, Liu O, Rowaihy H. Assigning sensors to missions with demands. In Algorithmic Aspects of Wireless Sensor Networks - Third International Workshop, ALGOSENSORS 2007, Revised Selected Papers. 2008. p. 114-125. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-540-77871-4_11