arXiv subjects

Noriyoshi Sukegawa

Publications and source records attributed to Noriyoshi Sukegawa.

At least 19 recordsLinked to original sources

arXiv2026

Condorcet-type properties of the linear ordering problem with ties

The Kemeny rule aggregates multiple strict rankings into a single strict ranking that minimizes the sum of its distances from the input rankings. The resulting optimization problem, called the Kemeny problem (\texttt{KP}), is a special case of the linear ordering problem (\texttt{LOP}). The Kemeny rule satisfies several desirable properties in social choice theory, including the extended Condorcet criterion (\texttt{XCC}). Ando et al. strengthened this result by introducing the strong Condorcet criterion (\texttt{SCC}) and showing that it holds for every optimal solution to an arbitrary \texttt{LOP} instance. Yoo and Escobedo extended the Kemeny rule to rankings with ties and showed that the resulting rule satisfies the non-strict extended Condorcet criterion (\texttt{NXCC}). This criterion gives a condition under which one candidate must be ranked strictly above another in every optimal solution. In this paper, we introduce the non-strict strong Condorcet criterion (\texttt{NSCC}), a counterpart of the \texttt{SCC} for rankings with ties, and show that it holds for every optimal solution to an arbitrary instance of the linear ordering problem with ties (\texttt{LOPT}). We also establish a complementary structural property that gives conditions under which two candidates must be tied in every optimal solution to an arbitrary \texttt{LOPT} instance.

cs.GT↗

arXiv2026

Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints

We study the problem of estimating multiple discrete unimodal distributions, motivated by search behavior analysis on a real-world platform. To incorporate prior knowledge of precedence relations among distributions, we impose stochastic order constraints and formulate the estimation task as a mixed-integer convex quadratic optimization problem. Experiments on both synthetic and real datasets show that the proposed method reduces the Jensen-Shannon divergence by 2.2% on average (up to 6.3%) when the sample size is small, while performing comparably to existing methods when sufficient data are available.

math.OC↗

arXiv2026

Decomposition-Based Constructive Heuristics for the Linear Ordering Problem

The linear ordering problem (LOP) is a classical NP-hard combinatorial optimization problem. In this paper, we study constructive heuristics for the LOP. We propose a unified recursive framework in which the index set is heuristically partitioned into smaller subsets, sufficiently small subproblems are solved exactly, and the resulting permutations are concatenated. Within this framework, we investigate three different recursive partitioning principles: a rule based on strongly connected components (the level graph method), a cut-based rule (the minimum cut method), and a score-based rule (the recursive Borda method). We first show that the recursive Borda method satisfies the Condorcet criterion, whereas the Borda rule does not. The level graph method and the minimum cut method satisfy a stronger Condorcet-type property, which the recursive Borda method does not satisfy. Computational experiments on xLOLIB instances show that the recursive Borda method provides the best average solution quality among the tested constructive heuristics. They also show that, after applying insertion-based local search, the differences in final solution quality among these heuristics become much smaller.

math.OC↗

arXiv2026

On the redundancy of transitivity constraints in the clique partitioning problem

In this study, we identify a class of redundant transitivity constraints in a 0-1 integer linear programming formulation of the clique partitioning problem. The transitivity constraints in this class can be removed from the formulation without changing the optimal solution set, although each transitivity constraint defines a facet of the associated polytope. This leads to a smaller formulation that is particularly effective for instances arising from correlation clustering, where edge weights are drawn from $\{-1,1\}$. Our computational experiments show that the resulting formulation outperforms existing formulations on such instances.

math.OC↗

arXiv2025

Subset Selection for Stratified Sampling in Online Controlled Experiments

Online controlled experiments, also known as A/B testing, are the digital equivalent of randomized controlled trials for estimating the impact of marketing campaigns on website visitors. Stratified sampling is a traditional technique for variance reduction to improve the sensitivity (or statistical power) of controlled experiments; this technique first divides the population into strata (homogeneous subgroups) based on stratification variables and then draws samples from each stratum to avoid sampling bias. To enhance the estimation accuracy of stratified sampling, we focus on the problem of selecting a subset of stratification variables that are effective in variance reduction. We design an efficient algorithm that selects stratification variables one by one by simulating a series of stratified sampling processes. We also estimate the computational complexity of our subset selection algorithm. Computational experiments using synthetic and real-world datasets demonstrate that our method can outperform other variance reduction techniques especially when multiple variables have a certain correlation with the outcome variable. Our subset selection method for stratified sampling can improve the sensitivity of online controlled experiments, thus enabling more reliable marketing decisions.

stat.CO↗

arXiv2024

Robust personalized pricing under uncertainty of purchase probabilities

This paper is concerned with personalized pricing models aimed at maximizing the expected revenues or profits for a single item. While it is essential for personalized pricing to predict the purchase probabilities for each consumer, these predicted values are inherently subject to unavoidable errors that can negatively impact the realized revenues and profits. To address this issue, we focus on robust optimization techniques that yield reliable solutions to optimization problems under uncertainty. Specifically, we propose a robust optimization model for personalized pricing that accounts for the uncertainty of predicted purchase probabilities. This model can be formulated as a mixed-integer linear optimization problem, which can be solved exactly using mathematical optimization solvers. We also develop a Lagrangian decomposition algorithm combined with line search to efficiently find high-quality solutions for large-scale optimization problems. Experimental results demonstrate the effectiveness of our robust optimization model and highlight the utility of our Lagrangian decomposition algorithm in terms of both computational efficiency and solution quality.

math.OC↗

arXiv2024

Strategic Coupon Allocation for Increasing Providers' Sales Experiences in Two-sided Marketplaces

In a two-sided marketplace, network effects are crucial for competitiveness, and platforms need to retain users through advanced customer relationship management as much as possible. Maintaining numerous providers' stable and active presence on the platform is highly important to enhance the marketplace's scale and diversity. The strongest motivation for providers to continue using the platform is to realize actual profits through sales. Then, we propose a personalized promotion to increase the number of successful providers with sales experiences on the platform. The main contributions of our research are twofold. First, we introduce a new perspective in provider management with the distribution of successful sales experiences. Second, we propose a personalized promotion optimization method to maximize the number of providers' sales experiences. By utilizing this approach, we ensure equal opportunities for providers to experience sales without being monopolized by a few providers. Through experiments using actual data on coupon distribution, we confirm that our method enables the implementation of coupon allocation strategies that significantly increase the total number of providers having sales experiences.

cs.IR↗

arXiv2024

Fast solution to the fair ranking problem using the Sinkhorn algorithm

In two-sided marketplaces such as online flea markets, recommender systems for providing consumers with personalized item rankings play a key role in promoting transactions between providers and consumers. Meanwhile, two-sided marketplaces face the problem of balancing consumer satisfaction and fairness among items to stimulate activity of item providers. Saito and Joachims (2022) devised an impact-based fair ranking method for maximizing the Nash social welfare based on fair division; however, this method, which requires solving a large-scale constrained nonlinear optimization problem, is very difficult to apply to practical-scale recommender systems. We thus propose a fast solution to the impact-based fair ranking problem. We first transform the fair ranking problem into an unconstrained optimization problem and then design a gradient ascent method that repeatedly executes the Sinkhorn algorithm. Experimental results demonstrate that our algorithm provides fair rankings of high quality and is about 1000 times faster than application of commercial optimization software.

cs.IR↗

arXiv2024

Container pre-marshalling problem minimizing CV@R under uncertainty of ship arrival times

This paper is concerned with the container pre-marshalling problem, which involves relocating containers in the storage area so that they can be efficiently loaded onto ships without reshuffles. In reality, however, ship arrival times are affected by various external factors, which can cause the order of container retrieval to be different from the initial plan. To represent such uncertainty, we generate multiple scenarios from a multivariate probability distribution of ship arrival times. We derive a mixed-integer linear optimization model to find an optimal container layout such that the conditional value-at-risk is minimized for the number of misplaced containers responsible for reshuffles. Moreover, we devise an exact algorithm based on the cutting-plane method to handle large-scale problems. Numerical experiments using synthetic datasets demonstrate that our method can produce high-quality container layouts compared with the conventional robust optimization model. Additionally, our algorithm can speed up the computation of solving large-scale problems.

math.OC↗

arXiv2024

Privacy-preserving recommender system using the data collaboration analysis for distributed datasets

In order to provide high-quality recommendations for users, it is desirable to share and integrate multiple datasets held by different parties. However, when sharing such distributed datasets, we need to protect personal and confidential information contained in the datasets. To this end, we establish a framework for privacy-preserving recommender systems using the data collaboration analysis of distributed datasets. Numerical experiments with two public rating datasets demonstrate that our privacy-preserving method for rating prediction can improve the prediction accuracy for distributed datasets. This study opens up new possibilities for privacy-preserving techniques in recommender systems.

cs.IR↗

arXiv2024

Robust portfolio optimization model for electronic coupon allocation

Currently, many e-commerce websites issue online/electronic coupons as an effective tool for promoting sales of various products and services. We focus on the problem of optimally allocating coupons to customers subject to a budget constraint on an e-commerce website. We apply a robust portfolio optimization model based on customer segmentation to the coupon allocation problem. We also validate the efficacy of our method through numerical experiments using actual data from randomly distributed coupons. Main contributions of our research are twofold. First, we handle six types of coupons, thereby making it extremely difficult to accurately estimate the difference in the effects of various coupons. Second, we demonstrate from detailed numerical results that the robust optimization model achieved larger uplifts of sales than did the commonly-used multiple-choice knapsack model and the conventional mean-variance optimization model. Our results open up great potential for robust portfolio optimization as an effective tool for practical coupon allocation.

cs.IR↗

arXiv2020

Predicting Online Item-choice Behavior: A Shape-restricted Regression Perspective

This paper examines the relationship between user pageview (PV) histories and their item-choice behavior on an e-commerce website. We focus on PV sequences, which represent time series of the number of PVs for each user--item pair. We propose a shape-restricted optimization model that accurately estimates item-choice probabilities for all possible PV sequences. This model imposes monotonicity constraints on item-choice probabilities by exploiting partial orders for PV sequences, according to the recency and frequency of a user's previous PVs. To improve the computational efficiency of our optimization model, we devise efficient algorithms for eliminating all redundant constraints according to the transitivity of the partial orders. Experimental results using real-world clickstream data demonstrate that our method achieves higher prediction performance than that of a state-of-the-art optimization model and common machine learning methods.

cs.IR↗

arXiv2019

The diameter of lattice zonotopes

We establish sharp asymptotic estimates for the diameter of primitive zonotopes when their dimension is fixed. We also prove that, for infinitely many integers $k$, the largest possible diameter of a lattice zonotope contained in the hypercube $[0,k]^d$ is uniquely achieved by a primitive zonotope. As a consequence, we obtain that this largest diameter grows like $k^{d/(d+1)}$ up to an explicit multiplicative constant, when $d$ is fixed and $k$ goes to infinity, providing a new lower bound on the largest possible diameter of a lattice polytope contained in $[0,k]^d$.

math.CO↗

arXiv2017

Improving bounds on the diameter of a polyhedron in high dimensions

In 1992, Kalai and Kleitman proved that the diameter of a $d$-dimensional polyhedron with $n$ facets is at most $n^{2+\log_2 d}$. In 2014, Todd improved the Kalai-Kleitman bound to $(n-d)^{\log_2 d}$. We improve the Todd bound to $(n-d)^{-1+\log_2 d}$ for $n \ge d \ge 7$, $(n-d)^{-2+\log_2 d}$ for $n \ge d \ge 37$, and $(n-d)^{-3+\log_2 d+O\left(1/d\right)}$ for $n \ge d \ge 1$.

math.OC↗

arXiv2016

A Latent-class Model for Estimating Product-choice Probabilities from Clickstream Data

This paper analyzes customer product-choice behavior based on the recency and frequency of each customer's page views on e-commerce sites. Recently, we devised an optimization model for estimating product-choice probabilities that satisfy monotonicity, convexity, and concavity constraints with respect to recency and frequency. This shape-restricted model delivered high predictive performance even when there were few training samples. However, typical e-commerce sites deal in many different varieties of products, so the predictive performance of the model can be further improved by integration of such product heterogeneity. For this purpose, we develop a novel latent-class shape-restricted model for estimating product-choice probabilities for each latent class of products. We also give a tailored expectation-maximization algorithm for parameter estimation. Computational results demonstrate that higher predictive performance is achieved with our latent-class model than with the previous shape-restricted model and common latent-class logistic regression.

cs.AI↗

arXiv2016

A simple proof of tail--polynomial bounds on the diameter of polyhedra

Let $Δ(d,n)$ denote the maximum diameter of a $d$-dimensional polyhedron with $n$ facets. In this paper, we propose a unified analysis of a recursive inequality about $Δ(d,n)$ established by Kalai and Kleitman in 1992. This yields much simpler proofs of a tail--polynomial and tail--almost--linear bounds on $Δ(d,n)$ which are recently discussed by Gallagher and Kim.

math.OC↗

arXiv2014

A primal-simplex based Tardos' algorithm

In the mid-eighties Tardos proposed a strongly polynomial algorithm for solving linear programming problems for which the size of the coefficient matrix is polynomially bounded by the dimension. Combining Orlin's primal-based modification and Mizuno's use of the simplex method, we introduce a modification of Tardos' algorithm considering only the primal problem and using simplex method to solve the auxiliary problems. The proposed algorithm is strongly polynomial if the coefficient matrix is totally unimodular and the auxiliary problems are non-degenerate.

math.OC↗

arXiv2014

Fractional programming formulation for the vertex coloring problem

We devise a new formulation for the vertex coloring problem. Different from other formulations, decision variables are associated with the pairs of vertices. Consequently, colors will be distinguishable. Although the objective function is fractional, it can be replaced by a piece-wise linear convex function. Numerical experiments show that our formulation has significantly good performance for dense graphs.

cs.DS↗