The complexity of finding most vital arcs and nodes
The complexity of finding most vital arcs and nodes
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Graph Algorithms
Approximation algorithms for the Label-CoverMAX and Red-Blue Set Cover problems
Journal of Discrete Algorithms
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs
ACM Transactions on Algorithms (TALG)
On the Positive--Negative Partial Set Cover problem
Information Processing Letters
Optimal Interdiction of Unreactive Markovian Evaders
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Submodular Function Minimization under Covering Constraints
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
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In network interdiction problems, evaders (e.g., hostile agents or data packets) may be moving through a network towards targets and we wish to choose locations for sensors in order to intercept the evaders before they reach their destinations. The evaders might follow deterministic routes or Markov chains, or they may be reactive, i.e., able to change their routes in order to avoid sensors placed to detect them. The challenge in such problems is to choose sensor locations economically, balancing security gains with costs, including the inconvenience sensors inflict upon innocent travelers. We study the objectives of 1) maximizing the number of evaders captured when limited by a budget on sensing cost and 2) capturing all evaders as cheaply as possible. We give optimal sensor placement algorithms for several classes of special graphs and hardness and approximation results for general graphs, including for deterministic or Markov chain-based and reactive or oblivious evaders. In a similar-sounding but fundamentally different problem setting posed by [7] where both evaders and innocent travelers are reactive, we again give optimal algorithms for special cases and hardness and approximation results on general graphs.