Maiko Shigeno

A new parameter for a broadcast algorithm with locally bounded Byzantine faults

This paper deals with broadcasting in a network with t-locally bounded Byzantine faults. One of the simplest broadcasting algorithms under Byzantine failures is referred to as a certified propagation algorithm (CPA), which is the only algorithm we know that does not use any global knowledge of the network topology. Hence, it is worth focusing on a graph-theoretic parameter such that CPA will work correctly. Using the theory of maximum adjacency (MA) ordering, a new graph-theoretic parameter for CPA is proposed. Within a factor of two, this parameter approximates the largest t such that CPA works for t-locally bounded Byzantine faults.

A comment on pure-strategy Nash equilibria in competitive diffusion games

In [N. Alon, M. Feldman, A.D. Procaccia, M. Tennenholtz, A note on competitive diffusion through social networks, Inform. Process. Lett. 110 (2010) 221-225], the authors introduced a game-theoretic model of diffusion process through a network. They showed a relation between the diameter of a given network and existence of pure Nash equilibria in the game. Theorem 1 of their paper says that a pure Nash equilibrium exists if the diameter is at most two. However, we have an example which does not admit a pure Nash equilibrium even if the diameter is two. Hence we correct the statement of Theorem 1 of their paper.

Conjugate Scaling Algorithm for Fenchel-Type Duality in Discrete Convex Optimization

This paper presents a polynomial time algorithm for solving submodular flow problems with a class of discrete convex cost functions. This class of problems is a common generalization of the submodular flow and valuated matroid intersection problems. The algorithm adopts a new scaling technique that scales the discrete convex cost functions via the conjugacy relation. The algorithm can be used to find a pair of optima in the form of the Fenchel-type duality theorem in discrete convex analysis.

Relaxed Most Negative Cycle and Most Positive Cut Canceling Algorithms for Minimum Cost Flow

This paper presents two new scaling algorithms for the minimum cost network flow problem, one a primal cycle canceling algorithm, the other a dual cut canceling algorithm. Both algorithms scale a relaxed optimality parameter, and create a second, inner relaxation. The primal algorithm uses the inner relaxation to cancel a most negative node-disjoint family of cycles w.r.t. the scaled parameter, the dual algorithm uses it to cancel most positive cuts w.r.t. the scaled parameter. We show that in a network with n nodes and m arcs, both algorithms need to cancel only Omn objects per scaling phase. Furthermore, we show how to efficiently implement both algorithms to yield weakly polynomial running times that are as fast as any other cycle or cut canceling algorithms. Our algorithms have potential practical advantages compared to some other canceling algorithms as well. Along the way, we give a comprehensive survey of cycle and cut canceling algorithms for min-cost flow. We also clarify the formal duality between cycles and cuts.

An algorithm for fractional assignment problems

Abstract In this paper, we propose a polynomial-time algorithm for fractional assignment problems. The fractional assignment problem is interpreted as follows. Let G = (I, J, E) be a bipartite graph where I and J are vertex sets and E ⊂- I × J is an edge set. We call an edge subset X(⊂- E) an assignment if every vertex is incident to exactly one edge from X. Given an integer weight cij and a positive integer weight dij for every edge (i, j)ϵ E, the fractional assignment problem finds an assignment X(⊂- E) such that the ratio (∑ (i, j)ϵX c ij ) (∑ (i, j)ϵX d ij ) is minimized. Some algorithms were developed for the fractional assignment problem. Recently, Radzik (1992) showed that an algorithm which is based on the parametric approach and Newtons method is the fastest one among them. Actually, it solves the fractional assignment problem in O ( nmlog 2 (nCD) (1 + log log(nCD) − log log(nD)) ) time where |I|=|J|=n, |E|=m, C = max{1, max{|cij|:(i, j)ϵ E}} and D = max{dij: (i, J)ϵ E} + 1. Our algorithm developed in this paper is also based on the parametric approach, but it is combined with the approximate binary search method. The time complexity of our algorithm is O ( nm log D log(nCD) ) time, and provides with a better time bound than the above algorithm.

A Strongly Polynomial Cut Canceling Algorithm for the Submodular Flow Problem

This paper presents a new strongly polynomial cut canceling algorithm for minimum cost submodular flow. The algorithm is a generalization of our similar cut canceling algorithm for ordinary mincost flow. The advantage of cut canceling over cycle canceling is that cut canceling seems to generalize to other problems more readily than cycle canceling. The algorithm scales a relaxed optimality parameter, and creates a second, inner relaxation that is a kind of submodular max flow problem. The outer relaxation uses a novel technique for relaxing the submodular constraints that allows our previous proof techniques to work. The algorithm uses the min cuts from the max flow subproblem as the relaxed most positive cuts it chooses to cancel. We show that this algorithm needs to cancel only O(n3) cuts per scaling phase, where n is the number of nodes. Furthermore, we also show how to slightly modify this algorithm to get a strongly polynomial running time.

The tree center problems and the relationship with the bottleneck knapsack problems

The tree center problems are designed to find a subtree minimizing the maximum distance from any vertex. This paper shows that these problems in a tree network are related to the bottleneck knapsack problems and presents linear-time algorithms for the tree center problems by using the relation.

A fast cost scaling algorithm for submodular flow

Abstract This paper presents the current fastest known weakly polynomial algorithm for the submodular flow problem when the costs are not too big. It combines Rocks or Bland and Jensens cost scaling algorithms, Cunningham and Franks primal-dual algorithm for submodular flow, and Fujishige and Zhangs push/relabel algorithm for submodular maximum flow to get a running time of O (n 4 h log C) , where n is the number of nodes, C is the largest absolute value of arc costs and h is the time for computing an exchange capacity in an instance of this problem.

Minimum Maximal Flow Problem: An Optimization over the Efficient Set

The network flow theory and algorithms have been developed on the assumption that each arc flow is controllable and we freely raise and reduce it. We however consider in this paper the situation where we are not able or allowed to reduce the given arc flow. Then we may end up with a maximal flow depending on the initial flow as well as the way of augmentation. Therefore the minimum of the flow values that are attained by maximal flows will play an important role to see how inefficiently the network can be utilized. We formulate this problem as an optimization over the efficient set of a multicriteria program, propose an algorithm, prove its finite convergence, and report on some computational experiments.

Maximum network flows with concave gains

This paper deals with a generalized maximum flow problem with concave gains, which is a nonlinear network optimization problem. Optimality conditions and an algorithm for this problem are presented. The optimality conditions are extended from the corresponding results for the linear gain case. The algorithm is based on the scaled piecewise linear approximation and on the fat path algorithm described by Goldberg, Plotkin and Tardos for linear gain cases. The proposed algorithm solves a problem with piecewise linear concave gains faster than the naive solution by adding parallel arcs.