8,447 research outputs found
Randomized Strategies for Robust Combinatorial Optimization
In this paper, we study the following robust optimization problem. Given an
independence system and candidate objective functions, we choose an independent
set, and then an adversary chooses one objective function, knowing our choice.
Our goal is to find a randomized strategy (i.e., a probability distribution
over the independent sets) that maximizes the expected objective value. To
solve the problem, we propose two types of schemes for designing approximation
algorithms. One scheme is for the case when objective functions are linear. It
first finds an approximately optimal aggregated strategy and then retrieves a
desired solution with little loss of the objective value. The approximation
ratio depends on a relaxation of an independence system polytope. As
applications, we provide approximation algorithms for a knapsack constraint or
a matroid intersection by developing appropriate relaxations and retrievals.
The other scheme is based on the multiplicative weights update method. A key
technique is to introduce a new concept called -reductions for
objective functions with parameters . We show that our scheme
outputs a nearly -approximate solution if there exists an
-approximation algorithm for a subproblem defined by
-reductions. This improves approximation ratio in previous
results. Using our result, we provide approximation algorithms when the
objective functions are submodular or correspond to the cardinality robustness
for the knapsack problem
Z-score-based modularity for community detection in networks
Identifying community structure in networks is an issue of particular
interest in network science. The modularity introduced by Newman and Girvan
[Phys. Rev. E 69, 026113 (2004)] is the most popular quality function for
community detection in networks. In this study, we identify a problem in the
concept of modularity and suggest a solution to overcome this problem.
Specifically, we obtain a new quality function for community detection. We
refer to the function as Z-modularity because it measures the Z-score of a
given division with respect to the fraction of the number of edges within
communities. Our theoretical analysis shows that Z-modularity mitigates the
resolution limit of the original modularity in certain cases. Computational
experiments using both artificial networks and well-known real-world networks
demonstrate the validity and reliability of the proposed quality function.Comment: 8 pages, 10 figure
Optimal Composition Ordering Problems for Piecewise Linear Functions
In this paper, we introduce maximum composition ordering problems. The input
is real functions and a constant
. We consider two settings: total and partial compositions. The
maximum total composition ordering problem is to compute a permutation
which maximizes , where .
The maximum partial composition ordering problem is to compute a permutation
and a nonnegative integer which maximize
.
We propose time algorithms for the maximum total and partial
composition ordering problems for monotone linear functions , which
generalize linear deterioration and shortening models for the time-dependent
scheduling problem. We also show that the maximum partial composition ordering
problem can be solved in polynomial time if is of form
for some constants , and . We
finally prove that there exists no constant-factor approximation algorithm for
the problems, even if 's are monotone, piecewise linear functions with at
most two pieces, unless P=NP.Comment: 19 pages, 4 figure
Improvement of measuring accuracy of magnetic field strength in single sheet testers by using two H coils
The accuracy of the measured magnetic field strength of single sheet testers using an H coil[1-4] is examined by finite element analysis. An improved measuring method which uses two H coils is proposed from this investigation. It is clarified that the best measuring method of magnetic field strength is the improved two H coil method. The validity of the new method is confirmed by experiments. </p
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