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?
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.