Competition in VM – Completing the Circle . Previous work in Competitive VM . Mainly follower’s perspective: given state (say of seed selection) of previous companies (agents/players): what’s the best strategy for the “follower” to maximize its spread in the face of the competition?
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Campaign runners don’t necessarily have unfettered access to the network!
There is an owner of the network.
Campaigns need owner’s permission.
May need to pay the owner.
I need 250 seeds
I need 100 seeds
Provides VM service.
Competition starts after host
How should the host select/allocate seeds?
JVC HD EverioGZ-VX815
For comparable products, if the b4b is substantially different,
dissatisfied company(ies) may take their VM business elsewhere!
Should I buy a
Which CC should
I’ve chosen my color!
Seeds influence out-neighbors (followers).
Active nodes influence followers.
Once influenced, relative weights of different (campaign) influences induce a
random decision making trial.
Nodes activated by time
My threshold is
Possible outcome at time
u 0.5 v 0.5 w 1.0 x
Red seed happens to
help blue’s cause!
u 0.5 v 0.5 w 1.0 x
Proof: Phase 1 logic influence propagation under classic LT model.
Observe, -- this prop. holds for WPCLT too!
-- seed selection (regardless of who gets which seed) can be done analogously to doing business in LT model.
-- decouple seed selection from allocation.
-- Next focus on allocation.
More formally, given the global seed set , partition it into subsets , such that:
Recall, bang for the buck for company
Adjusted Marginal Gain
Proof: Reduction from 3PARTITION: Given
pairwise disjoint :
3PARTITION is strongly NP-complete, i.e., is NP-complete even when is bounded by a polynomial in
Suppose a PTIME algorithm for FSA. Run it on the reduced instance above. The max b4biff the input instance is a YES-instance.
Input: S (with ) and
Output: A -partition of , with
1 Initialize ;
2 for each do
Can use a max-heap to run efficiently – in time.