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Polynomial time preprocessing to reduce instance size is one of the most commonly deployed heuristics to tackle computationally hard problems. In a parameterized problem, every instance I comes with a positive integer k. The problem is said to admit a polynomial kernel if, in polynomial time, we can reduce the size of the instance I to a polynomial in k, while preserving the answer. In this paper,...
We suggest a uniform game-theoretic approach to width graph parameters. We consider a search problem on a graph in which one cop in a helicopter flying from vertex to vertex tries to catch the robber. The existence of the winning program for the cop in this problem depends only on the robber's speed. We investigate the problem of finding the minimal robber's speed which prevents the cop from...
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