Lower and Upper Bounds for Minimum Energy ... - Semantic Scholar
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Lower and Upper Bounds for Minimum Energy Broadcast and Sensing Problems in Sensor Networks Guillaume Chelius — Eric Fleury — Thierry Mignon
N° 5072 January 2004
ISSN 0249-6399
ISRN INRIA/RR--5072--FR+ENG
THÈME 1
apport de recherche
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2
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Area(A(2η)) ≤ Area(A) 1 +
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.
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Unité de recherche INRIA Rhône-Alpes 655, avenue de l’Europe - 38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vignes 4, rue Jacques Monod - 91893 ORSAY Cedex (France) Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France) Unité de recherche INRIA Sophia Antipolis : 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France)
Éditeur INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France)
ISSN 0249-6399
Lower and Upper Bounds for Minimum Energy Broadcast and Sensing Problems in Sensor Networks Guillaume Chelius — Eric Fleury — Thierry Mignon
N° 5072 January 2004
ISSN 0249-6399
ISRN INRIA/RR--5072--FR+ENG
THÈME 1
apport de recherche
"!#$! %& ('*) +( ,- .0/ 2134 5 '7689*:$; !hìÖí2@ A
R = ∪(m,n)∈Z2 {D(Pj + mu + nv, rj ), j ∈ J}
'! ) #? 2 ) "=0 R
{D(Pj , rj ), j ∈ J}
?! u . v
hìÖí2@ A
2π √ 3 3
+? "! (R(η)) ≤ ατ "7 (B) + e(η) '! ) ) "! 3! ' " ? # .
limη→0 e(η) = 0
th0s}j\q B q}syr©ªq²ã{©± B ∩ A 6= ∅ ¸ n4j^ ºRj"*j\sRf®q thsurjku² ¯{sÀ ºRj"*²"Rqy.°³j^qrq yrfhsu sh¬4fqj©±qr¶wq.s}j3² ©±suiQj"yrj\4°³j^qrq@y}fhs η &Ь-j w©ªS yrf©ªq4©±yrfj*}j\"j\w©±kqj^Öy}©³R (Ö¸ τ + ε/2 efjQt©±u²su°³°(qtAfq RtAs}j. ºRj"q4² S ©±qsx"ºuj\ P ² A «0 uys©±j\À©± A(2η) = {x ∈ w©ªq|y A) < 2η} ¸ R ,§ ² A ©±(x, q½s"uikhsu y\« A(2η) s°ªqr©ªq"«Rsh.yrfjy}ys° q|y½u² P ©ªq(°±j\q}q9yrfhsu (τ +ε/2)Area(A(2η)) ¸ w©³h"j lim Area(A(2η)) »¼j "sy}su¶uj η qrthfyrfhsy = Area(A)
2
η→0
Area(A(2η)) ≤ Area(A) 1 +
ε 2(τ + ε/2)
.
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Unité de recherche INRIA Rhône-Alpes 655, avenue de l’Europe - 38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vignes 4, rue Jacques Monod - 91893 ORSAY Cedex (France) Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France) Unité de recherche INRIA Sophia Antipolis : 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France)
Éditeur INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France)
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