Kiyohito Nagano

Optimization for Centralized and Decentralized Cognitive Radio Networks

Cognitive radio technology improves radio resource usage by reconfiguring the wireless connection settings according to the optimum decisions, which are made on the basis of the collected context information. This paper focuses on optimization algorithms for decision making to optimize radio resource usage in heterogeneous cognitive wireless networks. For networks with centralized management, we proposed a novel optimization algorithm whose solution is guaranteed to be exactly optimal. In order to avoid an exponential increase of computational complexity in large-scale wireless networks, we model the target optimization problem as a minimum cost-flow problem and find the solution of the problem in polynomial time. For the networks with decentralized management, we propose a distributed algorithm using the distributed energy minimization dynamics of the Hopfield-Tank neural network. Our algorithm minimizes a given objective function without any centralized calculation. We derive the decision-making rule for each terminal to optimize the entire network. We demonstrate the validity of the proposed algorithms by several numerical simulations and the feasibility of the proposed schemes by designing and implementing them on experimental cognitive radio network systems.

Online prediction under submodular constraints

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 cardinality-based submodular functions, we give O(n2)-time algorithms.

A strongly polynomial algorithm for line search in submodular polyhedra

A submodular polyhedron is a polyhedron associated with a submodular function. This paper presents a strongly polynomial time algorithm for line search in submodular polyhedra with the aid of a fully combinatorial algorithm for submodular function minimization. The algorithm is based on the parametric search method proposed by Megiddo.

On Convex Minimization over Base Polytopes

This note considers convex optimization problems over base polytopes of polymatroids. We show that the decomposition algorithm for the separable convex function minimization problems helps us give simple sufficient conditions for the rationality of optimal solutions and that it leads us to some interesting properties, including the equivalence of the lexicographically optimal base problem, introduced by Fujishige, and the submodular utility allocation market problem, introduced by Jain and Vazirani. In addition, we develop an efficient implementation of the decomposition algorithm via parametric submodular function minimization algorithms. Moreover, we show that, in some remarkable cases, non-separable convex optimization problems over base polytopes can be solved in strongly polynomial time.

Submodular fractional programming for balanced clustering

We address the balanced clustering problem where cluster sizes are regularized with submodular functions. The objective function for balanced clustering is a submodular fractional function, i.e., the ratio of two submodular functions, and thus includes the well-known ratio cuts as special cases. In this paper, we present a novel algorithm for minimizing this objective function (submodular fractional programming) using recent submodular optimization techniques. The main idea is to utilize an algorithm to minimize the difference of two submodular functions, combined with the discrete Newton method. Thus, it can be applied to the objective function involving any submodular functions in both the numerator and the denominator, which enables us to design flexible clustering setups. We also give theoretical analysis on the algorithm, and evaluate the performance through comparative experiments with conventional algorithms by artificial and real datasets.