On the Resilience of Bipartite Networks

@article{Perkins2013OnTR,
  title={On the Resilience of Bipartite Networks},
  author={Will Perkins and L. Reyzin},
  journal={2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)},
  year={2013},
  pages={72-77}
}
  • Will PerkinsL. Reyzin
  • Published 24 June 2013
  • Mathematics
  • 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Motivated by problems modeling the spread of infections in networks, in this paper we explore which bipartite graphs are most resilient to widespread infections under various parameter settings. Namely, we study bipartite networks with a requirement of a minimum degree d on one side under an independent infection, independent transmission model. We completely characterize the optimal graphs in the case $d =1$, which already produces non-trivial behavior, and we give extremal results for the… 

Figures from this paper

Resilient Cyberphysical Systems and their Application Drivers: A Technology Roadmap

The focus is on design and deployment innovations that are broadly applicable across a range of CPS application areas, and through progressive learning, resilient-by-reaction.

Research Statement 1 Computational Learning Theory 1.1 Learning Languages and Automata

My research lies in computational learning theory, as well as in the broader fields of theoretical computer science and machine learning. A large fraction of my work focuses on what is called

References

SHOWING 1-10 OF 12 REFERENCES

Optimal network topologies for mitigating security and epidemic risks

  • A. HotaS. Sundaram
  • Mathematics, Computer Science
    2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
  • 2016
An upper bound on the expected number of vertices that are successfully attacked under the Nash equilibrium security investments in networked environments under security and epidemic risks is characterized, and graphs that minimize the fraction of infected vertices in steady state are characterized.

Network Formation in the Presence of Contagious Risk

It is found that socially optimal networks are situated just beyond a phase transition in the behavior of the cascading failures, and that stable graphs lie slightly further beyond this phase transition, at a point where most of the available welfare has been lost.

Random subgraphs of finite graphs: I. The scaling window under the triangle condition

Among the models for which the triangle diagram is small enough to allow us to draw these conclusions are the random graph, the n‐cube and certain Hamming cubes, as well as the spread‐out n‐dimensional torus for n > 6.

Clique partitions, graph compression and speeding-up algorithms

An interesting application of the graph compression result arises from the fact that several graph algorithms can be adapted to work with the compressed representation of the input graph, thereby improving the bound on their running times, particularly on dense graphs.

Percolation on finite graphs and isoperimetric inequalities

Consider a uniform expanders family Gn with a uniform bound on the degrees. It is shown that for any p and c>0, a random subgraph of Gn obtained by retaining each edge, randomly and independently,

Birth control for giants

Computer aided solutions to the possible differential equations for susceptibility allow us to establish lower and upper bounds on the extent to which the authors can either delay or accelerate the birth of the giant component.

Maximizing the spread of influence through a social network

An analysis framework based on submodular functions shows that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models, and suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.

Mean-Field Conditions for Percolation on Finite Graphs

AbstractLet {Gn} be a sequence of finite transitive graphs with vertex degree d = d(n) and |Gn| = n. Denote by pt(v, v) the return probability after t steps of the non-backtracking random walk on Gn.

On the completeness of a generalized matching problem

This work shows that if G contains a component with at least three vertices then this generalized matching problem is NP-complete, which has numerous applications including the minimization of second-order conflicts in examination scheduling.

Reducibility Among Combinatorial Problems

  • R. Karp
  • Computer Science
    50 Years of Integer Programming
  • 1972
Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.