Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Cyclic games and an algorithm to find minimax cycle means in directed graphs
USSR Computational Mathematics and Mathematical Physics
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
The network inhibition problem
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Cyclical games with prohibitions
Mathematical Programming: Series A and B
Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
The complexity of mean payoff games on graphs
Theoretical Computer Science
The complexity of finding most vital arcs and nodes
The complexity of finding most vital arcs and nodes
Mathematics of Operations Research
Scientific contributions of Leo Khachiyan (a short overview)
Discrete Applied Mathematics
Discrete Applied Mathematics
Non-oblivious strategy improvement
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
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We consider the problem of computing shortest paths in a directed arc-weighted graph G = (V,A) in the presence of an adversary that can block (interdict), for each vertex v ∈ V, a given number p(v) of the arcs Aout(v) leaving v. We show that if all arc-weights are non-negative then the single-destination version of the problem can be solved by a natural extension of Dijkstra's algorithm in time $$O(|A|+|V|{\rm log}|V|+\Sigma_{\upsilon\in{V}\ \backslash \{t\}}(|A_{out}(\upsilon)|-p(\upsilon)){\rm log}(p(\upsilon)+1)).$$ Our result can be viewed as a polynomial algorithm for a special case of the network interdiction problem where the adversary's budget is node-wise limited. When the adversary can block a given number p of arcs distributed arbitrarily in the graph, the problem (p-most-vital-arcs problem) becomes NP-hard. This result is also closely related to so-called cyclic games. No polynomial algorithm computing the value of a cyclic game is known, though this problem belongs to both NP and coNP.