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We consider an online prediction problem of combinatorial concepts where each combinatorial concept is represented as a vertex of a polyhedron described by a submodular function (base polyhedron). In general, there are exponentially many vertices in the base polyhedron. We propose polynomial time algorithms with regret bounds. In particular, for(More)
This paper proposes an algorithm for online linear optimization problem over permutations; the objective of the online algorithm is to find a permutation of {1,. .. , n} at each trial so as to minimize the " regret " for T trials. The regret of our algorithm is O(n 2 √ T ln n) in expectation for any input sequence. A naive implementation requires more than(More)
We discuss the problems to list, sample, and count the chordal graphs with edge constraints. The edge constraints are given as a pair of graphs one of which contains the other and one of which is chordal, and the objects we look at are the chordal graphs contained in one and containing the other. This setting is a natural generalization of chordal(More)
A general stochastic theory is presented for analysis of current records of a patch containing an arbitrary number (N) of independent homologous channels in the steady-state. We give the "basic theorem" that at the instant of any open (or shut) transition of a channel, the other N-1 channels are located in each state with a probability equal to those in the(More)
We show the existence of a polynomial-size extended formulation for the base polytope of a (k, ℓ)-sparsity matroid. For an undirected graph G = (V, E), the size of the formulation is O(|V ||E|) when k ≥ ℓ and O(|V | 2 |E|) when k ≤ ℓ. To this end, we employ the technique developed by Faenza et al. recently that uses a randomized communication protocol.