Sharing the cost of multicast transmissions in wireless networks
This presentation is the property of its rightful owner.
Sponsored Links
1 / 21

Sharing the cost of multicast transmissions in wireless networks PowerPoint PPT Presentation


  • 106 Views
  • Uploaded on
  • Presentation posted in: General

Sharing the cost of multicast transmissions in wireless networks. Carmine Ventre Joint work with Paolo Penna University of Salerno, WP2. Wireless transmission. Power(i)= d(i,j) α = range(i) α , α>1 (empty space α = 2 )

Download Presentation

Sharing the cost of multicast transmissions in wireless networks

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Sharing the cost of multicast transmissions in wireless networks

Sharing the cost of multicast transmissions in wireless networks

Carmine Ventre

Joint work with

Paolo Penna

University of Salerno, WP2


Wireless transmission

Wireless transmission

  • Power(i)= d(i,j)α = range(i) α, α>1 (empty space α = 2)

  • A message sent by station i to j can be also received by every station in transmission range of i

d(i,j)α

i

j


Wireless multicast transmission

Wireless multicast transmission

known

10€

1€

1€

3€

source

Paolo 1€

Carmine 1€

Christos 10€

Andrea 30€

Pino 50€

  • Who receives Roma-Juventus

  • How to transmit

  • Goal: maximize

    Benefit – Cost

    i.e. the social welfare

private


Selfish agents

Selfish agents

WYSWYP (What You Say What You Pay)

source

  • COST = 10 + 5 = 15

  • WORTH = 50 + 30 = 80

  • NET WORTH = 80 – 15 = 65

10

0 €

Pino 50 €

5

5.1 €

Pino says 0 € and gets

Roma – Juventus

for free

Andrea says 5.1 €

Pino says 0 €

Andrea says 5.1 € and gets

Roma – Juventus

for a lower price

Andrea 30 €

Nobody gets

Roma - Juventus

10

Paolo 9 €

NW’ = 0


Graph model

Graph model

  • A complete directed weighted communication graph G=(S,E,w)

  • w(i,j) = cost of link (i,j)

    • w(1,4) = d(1,4)2.1

    • w(1,2) = d(1,2)5

    • w(2,4) = ∞

    • w(4,2) = d(4,2)2.1

  • A source node s

  • vi = private valuation of agent i

v1

1

2

v2

v3

v4

4

3


Mechanism design model

Mechanism design: model

  • Design a mechanism M=(A,P)

    • Each agent declares bi

    • Algorithm A selects, based on (b1, …, bn),

      • a set of receivers

      • a subset of connection T  E

    • Agent i must pay Pi(b1, …, bi-1, bi, bi+1 ..., bn)

  • Utility of the agent

    ui(bi)=

  • Goal of agent i: maximize ui(bi)


Mechanism s desired properties

Mechanism’s desired properties

  • No positive transfer (NPT)

    • Payments are nonnegative: Pi  0

  • Voluntary Participation (VP)

    • User i is charged less then his reported valuation bi (i.e. bi≥ Pi)

  • Consumer Sovereignty (CS)

    • Each user can receive the transmission if he is willing to pay a high price.


Mechanism s desired properties incentive compatibility

Mechanism’s desired properties: Incentive Compatibility

  • Strategyproof (truthful) mechanism

    • Telling the true vi is a dominant strategy for any agent

  • Group-strategyproof mechanism

    • No coalition of agents has an incentive to jointly misreport their true viStronger form of Incentive Compatibility.


Mechanism s desired properties1

Mechanism’s desired properties

  • Budget Balance (BB)

    • Pi = COST(T) (where T is the solution set)

  • Efficiency (NW)

    • the mechanism should maximize the

      NET WORTH(T) := WORTH(T)-COST(T)

      whereWORTH(T):= iT vj

Mutually exclusive!!

Efficiency No Group strategy-proof


Previous work

Previous work

Wireless broadcast

  • 1d: COSTopt in polynomial time [Clementi et al, to appear]

  • 2d: NP-hard, MST is an O(1)-apx [Clementi et al, ‘01]

  • On graphs: (log n)-apx [Guha et al ‘96, Caragiannis et al, ‘02]

  • Many others…

    Wired cost sharing (selfish receivers)

  • Distributed polytime truthful, efficient, NPT, VP, and CS mechanism for trees (no BB) [Feigenbaum et al, ‘99]

  • Budget balance, NPT, VP, CS and group strategy-proof mechanism (no efficiency) [Jain et al, ‘00]

  • No α-efficiency and β-BB for each α, β > 1 [Feigenbaum et al, ‘02]

  • polytime algorithm  no R-efficiency, for each R > 1 [Feigenbaum et al, ‘99]


Our results

Our results

G is a tree

  • NWopt in polytime distributed algorithm

  • Polytime mechanism M=(A,P) truthful, NPT, VP and CS

  • Extensions to “metric trees” graphs

    G is not a tree

  • 2d: NP-hard to compute NWopt

  • 1d: Polytime mechanism M=(A,P) truthful, NPT, VP, CS and efficient (i.e. NW is maximized)

  • Precompute an universal multicast tree T  G

    • A polytime truthful, NPT, VP and CS mechanism

    • O(1) or O(n)-efficiency, in some cases

  • polytime algorithm  no R-efficiency, for every R > 1


Vcg trick marginal cost mechanism

VCG Trick (marginal cost mechanism)

  • Utilitarian problem:

    •  Xsol, measure(X)=i valuationi(X)

  • Aoptcomputes Xsol maximizing measure(X)

  • PVCG: M=(Aopt, PVCG) is truthful


Vcg trick marginal cost mechanism1

VCG Trick (marginal cost mechanism)

Making our problem utilitarian:

= i

measure(X)

valuationi(X)

iX

WORTH(X)-COST(X)

vi

- ci

= WORTH(X)

- COST(X)

Initially, charge to every receiver i

the cost ci of its ingoing connection

ci

Pi = ci + PVCG

vi


Free edges on trees

Free edges on Trees

RECURSION?

tree

graph

s

s

1

2

3

1

2

3

4

5

4

5

4

5

4

5

3

4

3

4

YES!

NO!


Trees algorithm recursive equation

Trees algorithm: recursive equation

  • It is easy to see that the best solution has an optimal substructure

  • It is simple to compute NWopt(s) in distributed bottom-up fashion

  • O(n) time, 2 msgs per link

vi

i

cj

j

k s.t. ck≤ cj


Trees with metric free edges

Trees with metric free edges

  • Path(i,4)=w(i,1)+w(1,4)

  • w(i,3) ≥ path(i,4)

  • (i,4) metric free edge

i

7

5

6

1

2

3

1

5

4

5


Tree with metric free edge idea

Tree with metric free edge: idea

  • A node k reached for free gets some credit

i

k gets cj-ck

units of credit

ck

cj

k

j


Tree with metric free edge credit usage

Tree with metric free edge: credit usage

k

  • k can use its credit to reach all of its children

  • If there is a child l s.t. cl > credit(k) and NWopt(l)>0 then credit(k) is useless

    • For each r Є ch(k): cl – cr > credit(k) – cr

  • Paying a free edge is not a good solution (i.e. we have a smallest credit and a greater cost)

credit(r) = credit(k)-cr

r

k

r

l

credit(r)=cl-cr

credit(l)=0


Tree with metric free edge recursive equations

Tree with metric free edge: recursive equations

  • We have two contributions:

    • the nodes whose ingoing edge is paid

    • the nodes with credit c whose ingoing edge is free

NOTE: the optimum is NWopt(s,0)


The one dimensional euclidean case

The one dimensional Euclidean case

  • Stations located on a line (linear network)

1

i

j

n

s

receivers

Clementi et al algo


Some open problems

(Some) Open problems

  • 2d Euclidean case:

    • O(1)-APX multicast algorithm

    • “Good” universal Euclidean multicast trees

    • Truthful mechanism with O(1)-APX

    • BB truthful mechanisms


  • Login