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- W2578358450 abstract "We think of a tournament T = ([n];E) as a communication network where in each round of communication processor Pi sends its information to Pj, for every directed edge ij ∈ E(T). By Landau’s theorem (1953) there is a King in T, i.e., a processor whose initial input reaches every other processor in two rounds or less. Namely, a processor P such that after two rounds of communication along T’s edges, the initial information of P reaches all other processors. Here we consider a more general scenario where an adversary selects an arbitrary series of tournaments T1;T2;:::, so that in each round s = 1;2;:::, communication is governed by the corresponding tournament Ts. We prove that for every series of tournaments that the adversary selects, it is still true that after two rounds of communication, the initial input of at least one processor reaches everyone. Concretely, we show that for every two tournaments T1;T2 there is a vertex in [n] that can reach all vertices via (i) A step in T1, or (ii) A step in T2 or (iii) A step in T1 followed by a step in T2." @default.
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- W2578358450 date "2012-01-01" @default.
- W2578358450 modified "2023-09-27" @default.
- W2578358450 title "A King in every two consecutive tournaments" @default.
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- W2578358450 hasPublicationYear "2012" @default.
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