136 research outputs found
Approximately Stable Matchings with Budget Constraints
This paper considers two-sided matching with budget constraints where one
side (firm or hospital) can make monetary transfers (offer wages) to the other
(worker or doctor). In a standard model, while multiple doctors can be matched
to a single hospital, a hospital has a maximum quota: the number of doctors
assigned to a hospital cannot exceed a certain limit. In our model, a hospital
instead has a fixed budget: the total amount of wages allocated by each
hospital to doctors is constrained. With budget constraints, stable matchings
may fail to exist and checking for the existence is hard. To deal with the
nonexistence of stable matchings, we extend the "matching with contracts" model
of Hatfield and Milgrom, so that it handles approximately stable matchings
where each of the hospitals' utilities after deviation can increase by factor
up to a certain amount. We then propose two novel mechanisms that efficiently
return such a stable matching that exactly satisfies the budget constraints. In
particular, by sacrificing strategy-proofness, our first mechanism achieves the
best possible bound. Furthermore, we find a special case such that a simple
mechanism is strategy-proof for doctors, keeping the best possible bound of the
general case.Comment: Accepted for the 32nd AAAI Conference on Artificial Intelligence
(AAAI2018). arXiv admin note: text overlap with arXiv:1705.0764
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
Additive Approximation Algorithms for Modularity Maximization
The modularity is a quality function in community detection, which was
introduced by Newman and Girvan (2004). Community detection in graphs is now
often conducted through modularity maximization: given an undirected graph
, we are asked to find a partition of that maximizes
the modularity. Although numerous algorithms have been developed to date, most
of them have no theoretical approximation guarantee. Recently, to overcome this
issue, the design of modularity maximization algorithms with provable
approximation guarantees has attracted significant attention in the computer
science community.
In this study, we further investigate the approximability of modularity
maximization. More specifically, we propose a polynomial-time
-additive approximation algorithm for the
modularity maximization problem. Note here that
holds. This improves the current best additive approximation error of ,
which was recently provided by Dinh, Li, and Thai (2015). Interestingly, our
analysis also demonstrates that the proposed algorithm obtains a nearly-optimal
solution for any instance with a very high modularity value. Moreover, we
propose a polynomial-time -additive approximation algorithm for the
maximum modularity cut problem. It should be noted that this is the first
non-trivial approximability result for the problem. Finally, we demonstrate
that our approximation algorithm can be extended to some related problems.Comment: 23 pages, 4 figure
Applying Geographically Weighted Regression to Conjoint Analysis: Empirical Findings from Urban Park Amenities
The objective of this study is to develop spatially-explicit choice model and investigate its validity and applicability in CA studies. This objective is achieved by applying locally-regressed geographically weighted regression (GWR) and GIS to survey data on hypothetical dogrun facilities (off-leash dog area) in urban recreational parks in Tokyo, Japan. Our results show that spatially-explicit conditional logit model developed in this study outperforms traditional model in terms of data fit and prediction accuracy. Our results also show that marginal willingness-to-pay for various attributes of dogrun facilities has significant spatial variation. Analytical procedure developed in this study can reveal spatially-varying individual preferences on attributes of urban park amenities, and facilitates area-specific decision makings in urban park planning.Choice experiments, conjoint analysis, dogrun, geographically weighted regression, spatial econometrics, Research Methods/ Statistical Methods, Resource /Energy Economics and Policy,
Surrogate Optimization for p-Norms
In this paper, we study the effect of surrogate objective functions in optimization problems. We introduce surrogate ratio as a measure of such effect, where the surrogate ratio is the ratio between the optimal values of the original and surrogate objective functions.
We prove that the surrogate ratio is at most mu^{|1/p - 1/q|} when the objective functions are p- and q-norms, and the feasible region is a mu-dimensional space (i.e., a subspace of R^mu), a mu-intersection of matroids, or a mu-extendible system. We also show that this is the best possible bound. In addition, for mu-systems, we demonstrate that the ratio becomes mu^{1/p} when p q. Here, a mu-system is an independence system such that for any subset of ground set the ratio of the cardinality of the largest to the smallest maximal independent subset of it is at most mu. We further extend our results to the surrogate ratios for approximate solutions
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