arXiv subjects

Kazuya Haraguchi

Publications and source records attributed to Kazuya Haraguchi.

At least 19 recordsLinked to original sources

arXiv2026

Fast Enumeration of Minimal Removable Sets in Monotone Systems with Application to Core Collapse Analysis

In network vulnerability analysis, it is crucial to evaluate the robustness of $k$-cores against vertex removals. A $k$-core is often fragile since removing a few vertices can trigger a large reduction in the core size, a phenomenon known as core collapse. In this paper, we study the problem of enumerating all minimal removable sets (MinRSs) of a given $k$-core, where a MinRS is a minimal nonempty set of vertices whose removal results in a smaller $k$-core graph. We consider this problem within a general mathematical framework based on monotone systems. We show that, for a monotone system that is given with an underlying graph $G=(V,E)$, all MinRSs of a solution can be enumerated in $O((n+m)nτ_ω)$ time, where $n=|V|$, $m=|E|$ and $τ_ω$ denotes the computation time of evaluating the monotone function of the system. Furthermore, if the system satisfies the newly defined in-dominating seed property, the complexity drops to $O((n+m) \log n \cdot τ_ω)$ time. We prove that standard $k$-cores in undirected graphs satisfy this property, enabling MinRS enumeration in $O((n+m)\log n)$ time, a significant improvement over the baseline. We also extend our framework to enumerate all solutions in a given monotone system. This yields an $O((n+m)\log n)$-delay algorithm for all $k$-core subgraphs, outperforming an algorithm given by [Boley et al., Theoretical Computer Science, 2010]. Our framework is applicable to various $k$-core extensions, including weighted $k$-cores, multi-layer $\boldsymbol{k}$-cores, and $(k,\ell)$-cores.

cs.DS↗

arXiv2026

Mixing Vector Model for Copolymer Inference via Mixed Integer Linear Programming

A novel two-phase molecule inference framework, mol-infer, has recently been developed to infer chemical graphs with prescribed abstract structures and desired property values through mixed integer linear programming (MILP) under the two-layered model, with guaranteed optimality and exactness relative to the given learned prediction function and structural constraints. In this study, we extend this framework to copolymers by introducing a simple feature representation, called the mixing vector (MV) model. In the proposed model, a copolymer feature vector is represented as a convex combination of MILP-tractable monomer descriptors weighted by the mixing ratio of the constituent monomers. This representation does not require explicit sequence-class information and is therefore naturally compatible with MILP-based inverse design. Under this model, we construct prediction functions for several copolymer property datasets using artificial neural networks, reduced quadratic multiple linear regression, and random forests. The proposed representation achieves practically useful predictive performance across multiple physicochemical property datasets; in particular, the best test R^2 score exceeds 0.7 for nine of the ten datasets and exceeds 0.9 for six datasets. We also formulate a multi-monomer inverse-design problem under the MV representation with a prescribed mixing ratio and show that the resulting MILP instances remain tractable, even for three-monomer settings. Finally, we perform an external consistency check by re-evaluating the inferred candidates and comparing the re-computed property values with those predicted by the learned model. Overall, the proposed framework gives a tractable first step toward model-level exact inverse design of copolymers under the two-layered model.

q-bio.QM↗

arXiv2025

The Minimum Number of Edges in $(p+1)K_2$-Saturated Graphs

Given a family of graphs $\mathcal{F}$, a graph $G$ is $\mathcal{F}$-saturated if it is $\mathcal{F}$-free but the addition of any missing edge creates a copy of some $F \in \mathcal{F}$. The study of the minimum number of edges in $\mathcal{F}$-saturated graphs is a central topic in extremal graph theory. Let $(p+1)K_2$ denote a matching of size $p+1$. Determining the minimum number of edges in a $(p+1)K_{2}$-saturated graph is a fundamental question in this area, explicitly posed as Problem 9 in the survey by Faudree et al. (2011). In this paper, we refine the structural analysis of $(p+1)K_2$-saturated graphs and derive an explicit formula for the number of edges in terms of a single integer parameter. By minimizing this formula we determine $\mathrm{sat}(n,(p+1)K_2)$ for all $n>2p$, thereby resolving Problem 9 in full generality and extending earlier results of Kászonyi--Tuza (1986) and Zhang--Lu--Yu (2024). Moreover, by maximizing the same formula we recover the classical Erdős--Gallai (1959) upper bound on the number of edges in such graphs.

math.CO↗

arXiv2025

Enumeration of Bases in Matroid with Exponentially Large Ground Set

When we deal with a matroid ${\mathcal M}=(U,{\mathcal I})$, we usually assume that it is implicitly given by means of the independence (IND) oracle. Time complexity of many existing algorithms is polynomially bounded with respect to $|U|$ and the running time of the IND-oracle. However, they are not efficient any more when $U$ is exponentially large in some context. In this paper, we propose two algorithms for enumerating matroid bases such that the time complexity does not depend on $|U|$. For some integer $L$, the first algorithm enumerates the first $L$ minimum-weight bases in incremental-polynomial time and the remaining ones in polynomial-delay. To design the algorithm, we assume two oracles other than the IND-oracle: the MinB-oracle that returns a minimum basis and the REL-oracle that returns a relevant element one by one in non-decreasing order of weight. The proposed algorithm is applicable to enumeration of minimum bases of binary matroids from cycle space and cut space, all of which have exponentially large $U$ with respect to a given graph. The highlight in this context is that, to design the REL-oracle for cut space, we develop the first polynomial-delay algorithm that enumerates all relevant cuts of a given graph in non-decreasing order of weight. The second algorithm enumerates all sets of linearly independent $r$-dimensional $r$ vectors over $\mathit{GF}(2)$ in polynomial-delay, which immediately yields a polynomial-delay algorithm %%with respect to the matroid rank $r$ that enumerates all unweighted bases of a binary matroid such that elements are closed under addition.

cs.DS↗

arXiv2025

Combining Graph Neural Networks and Mixed Integer Linear Programming for Molecular Inference under the Two-Layered Model

Recently, a novel two-phase framework named mol-infer for inference of chemical compounds with prescribed abstract structures and desired property values has been proposed. The framework mol-infer is primarily based on using mixed integer linear programming (MILP) to simulate the computational process of machine learning methods and describe the necessary and sufficient conditions to ensure such a chemical graph exists. The existing approaches usually first convert the chemical compounds into handcrafted feature vectors to construct prediction functions, but because of the limit on the kinds of descriptors originated from the need for tractability in the MILP formulation, the learning performances on datasets of some properties are not good enough. A lack of good learning performance can greatly lower the quality of the inferred chemical graphs, and thus improving learning performance is of great importance. On the other hand, graph neural networks (GNN) offer a promising machine learning method to directly utilize the chemical graphs as the input, and many existing GNN-based approaches to the molecular property prediction problem have shown that they can enjoy better learning performances compared to the traditional approaches that are based on feature vectors. In this study, we develop a molecular inference framework based on mol-infer, namely mol-infer-GNN, that utilizes GNN as the learning method while keeping the great flexibility originated from the two-layered model on the abstract structure of the chemical graph to be inferred. We conducted computational experiments on the QM9 dataset to show that our proposed GNN model can obtain satisfying learning performances for some properties despite its simple structure, and can infer small chemical graphs comprising up to 20 non-hydrogen atoms within reasonable computational time.

cs.LG↗

arXiv2025

Towards Environment-Sensitive Molecular Inference via Mixed Integer Linear Programming

Traditional QSAR/QSPR and inverse QSAR/QSPR methods often assume that chemical properties are dictated by single molecules, overlooking the influence of molecular interactions and environmental factors. In this paper, we introduce a novel QSAR/QSPR framework that can capture the combined effects of multiple molecules (e.g., small molecules or polymers) and experimental conditions on property values. We design a feature function to integrate the information of multiple molecules and the environment. Specifically, for the property Flory-Huggins $χ$-parameter, which characterizes the thermodynamic properties between the solute and the solvent, and varies in temperatures, we demonstrate through computational experimental results that our approach can achieve a competitively high learning performance compared to existing works on predicting $χ$-parameter values, while inferring the solute polymers with up to 50 non-hydrogen atoms in their monomer forms in a relatively short time. A comparison study with the simulation software J-OCTA demonstrates that the polymers inferred by our methods are of high quality.

physics.chem-ph↗

arXiv2024

Systematic evaluation of the isolated effect of tissue environment on the transcriptome using a single-cell RNA-seq atlas dataset

Background: Understanding cellular diversity throughout the body is essential for elucidating the complex functions of biological systems. Recently, large-scale single-cell omics datasets, known as omics atlases, have become available. These atlases encompass data from diverse tissues and cell-types, providing insights into the landscape of cell-type-specific gene expression. However, the isolated effect of the tissue environment has not been thoroughly investigated. Evaluating this isolated effect is challenging due to statistical confounding with cell-type effects, arising from significant biases in the combinations of tissues and cell-types within the body. Results: This study introduces a novel data analysis framework, named the Combinatorial Sub-dataset Extraction for Confounding Reduction (COSER), which addresses statistical confounding by using graph theory to enumerate appropriate sub-datasets. COSER enables the assessment of isolated effects of discrete variables in single cells. Applying COSER to the Tabula Muris Senis single-cell transcriptome atlas, we characterized the isolated impact of tissue environments. Our findings demonstrate that some of genes are markedly affected by the tissue environment, particularly in modulating intercellular diversity in immune responses and their age-related changes. Conclusion: COSER provides a robust, general-purpose framework for evaluating the isolated effects of discrete variables from large-scale data mining. This approach reveals critical insights into the interplay between tissue environments and gene expression.

q-bio.GN↗

arXiv2024

SSD Set System, Graph Decomposition and Hamiltonian Cycle

In this paper, we first study what we call Superset-Subset-Disjoint (SSD) set system. Based on properties of SSD set system, we derive the following (I) to (IV): (I) For a nonnegative integer $k$ and a graph $G=(V,E)$ with $|V|\ge2$, let $X_1,X_2,\dots,X_q\subsetneq V$ denote all maximal proper subsets of $V$ that induce $k$-edge-connected subgraphs. Then at least one of (a) and (b) holds: (a) $\{X_1,X_2,\dots,X_q\}$ is a partition of $V$; and (b) $V\setminus X_1, V\setminus X_2,\dots,V\setminus X_q$ are pairwise disjoint. (II) For $k=1$ and a strongly-connected digraph $G$, whether $V$ is in (a) and/or (b) can be decided in $O(n+m)$ time and we can generate all such $X_1,X_2,\dots,X_q$ in $O(n+m+|X_1|+|X_2|+\dots+|X_q|)$ time, where $n=|V|$ and $m=|E|$. (III) For a digraph $G$, we can enumerate in linear delay all vertex subsets of $V$ that induce strongly-connected subgraphs. (IV) A digraph is Hamiltonian if there is a spanning subgraph that is strongly-connected and in the case (a).

cs.DS↗

arXiv2024

A Unified Approach to Inferring Chemical Compounds with the Desired Aqueous Solubility

Aqueous solubility (AS) is a key physiochemical property that plays a crucial role in drug discovery and material design. We report a novel unified approach to predict and infer chemical compounds with the desired AS based on simple deterministic graph-theoretic descriptors, multiple linear regression (MLR) and mixed integer linear programming (MILP). Selected descriptors based on a forward stepwise procedure enabled the simplest regression model, MLR, to achieve significantly good prediction accuracy compared to the existing approaches, achieving the accuracy in the range [0.7191, 0.9377] for 29 diverse datasets. By simulating these descriptors and learning models as MILPs, we inferred mathematically exact and optimal compounds with the desired AS, prescribed structures, and up to 50 non-hydrogen atoms in a reasonable time range [6, 1204] seconds. These findings indicate a strong correlation between the simple graph-theoretic descriptors and the AS of compounds, potentially leading to a deeper understanding of their AS without relying on widely used complicated chemical descriptors and complex machine learning models that are computationally expensive, and therefore difficult to use for inference. An implementation of the proposed approach is available at https://github.com/ku-dml/mol-infer/tree/master/AqSol.

cs.LG↗

arXiv2024

Cycle-Configuration: A Novel Graph-theoretic Descriptor Set for Molecular Inference

In this paper, we propose a novel family of descriptors of chemical graphs, named cycle-configuration (CC), that can be used in the standard "two-layered (2L) model" of mol-infer, a molecular inference framework based on mixed integer linear programming (MILP) and machine learning (ML). Proposed descriptors capture the notion of ortho/meta/para patterns that appear in aromatic rings, which has been impossible in the framework so far. Computational experiments show that, when the new descriptors are supplied, we can construct prediction functions of similar or better performance for all of the 27 tested chemical properties. We also provide an MILP formulation that asks for a chemical graph with desired properties under the 2L model with CC descriptors (2L+CC model). We show that a chemical graph with up to 50 non-hydrogen vertices can be inferred in a practical time.

cs.LG↗

arXiv2023

Molecular Design Based on Integer Programming and Splitting Data Sets by Hyperplanes

A novel framework for designing the molecular structure of chemical compounds with a desired chemical property has recently been proposed. The framework infers a desired chemical graph by solving a mixed integer linear program (MILP) that simulates the computation process of a feature function defined by a two-layered model on chemical graphs and a prediction function constructed by a machine learning method. To improve the learning performance of prediction functions in the framework, we design a method that splits a given data set $\mathcal{C}$ into two subsets $\mathcal{C}^{(i)},i=1,2$ by a hyperplane in a chemical space so that most compounds in the first (resp., second) subset have observed values lower (resp., higher) than a threshold $θ$. We construct a prediction function $ψ$ to the data set $\mathcal{C}$ by combining prediction functions $ψ_i,i=1,2$ each of which is constructed on $\mathcal{C}^{(i)}$ independently. The results of our computational experiments suggest that the proposed method improved the learning performance for several chemical properties to which a good prediction function has been difficult to construct.

cs.CE↗

arXiv2023

A Linear Delay Algorithm for Enumeration of 2-Edge/Vertex-connected Induced Subgraphs

For a set system $(V,{\mathcal C}\subseteq 2^V)$, we call a subset $C\in{\mathcal C}$ a component. A nonempty subset $Y\subseteq C$ is a minimal removable set (MRS) of $C$ if $C\setminus Y\in{\mathcal C}$ and no proper nonempty subset $Z\subsetneq Y$ satisfies $C\setminus Z\in{\mathcal C}$. In this paper, we consider the problem of enumerating all components in a set system such that, for every two components $C,C'\in{\mathcal C}$ with $C'\subsetneq C$, every MRS $X$ of $C$ satisfies either $X\subseteq C'$ or $X\cap C'=\emptyset$. We provide a partition-based algorithm for this problem, which yields the first linear delay algorithms to enumerate all 2-edge-connected induced subgraphs, and to enumerate all 2-vertex-connected induced subgraphs.

cs.DS↗

arXiv2022

Molecular Design Based on Integer Programming and Quadratic Descriptors in a Two-layered Model

A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property, where design of novel drugs is an important topic in bioinformatics and chemo-informatics. The framework infers a desired chemical graph by solving a mixed integer linear program (MILP) that simulates the computation process of a feature function defined by a two-layered model on chemical graphs and a prediction function constructed by a machine learning method. A set of graph theoretical descriptors in the feature function plays a key role to derive a compact formulation of such an MILP. To improve the learning performance of prediction functions in the framework maintaining the compactness of the MILP, this paper utilizes the product of two of those descriptors as a new descriptor and then designs a method of reducing the number of descriptors. The results of our computational experiments suggest that the proposed method improved the learning performance for many chemical properties and can infer a chemical structure with up to 50 non-hydrogen atoms.

q-bio.BM↗

arXiv2022

Polynomial-delay Enumeration Algorithms in Set Systems

We consider a set system $(V, {\mathcal C}\subseteq 2^V)$ on a finite set $V$ of elements, where we call a set $C\in {\mathcal C}$ a component. We assume that two oracles $\mathrm{L}_1$ and $\mathrm{L}_2$ are available, where given two subsets $X,Y\subseteq V$, $\mathrm{L}_1$ returns a maximal component $C\in {\mathcal C}$ with $X\subseteq C\subseteq Y$; and given a set $Y\subseteq V$, $\mathrm{L}_2$ returns all maximal components $C\in {\mathcal C}$ with $C\subseteq Y$. Given a set $I$ of attributes and a function $σ:V\to 2^I$ in a transitive system, a component $C\in {\mathcal C}$ is called a solution if the set of common attributes in $C$ is inclusively maximal; i.e., $\bigcap_{v\in C}σ(v)\supsetneq \bigcap_{v\in X}σ(v)$ for any component $X\in{\mathcal C}$ with $C\subsetneq X$. We prove that there exists an algorithm of enumerating all solutions (or all components) in delay bounded by a polynomial with respect to the input size and the running times of the oracles.

cs.DM↗

arXiv2021

A Method for Inferring Polymers Based on Linear Regression and Integer Programming

A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property using both artificial neural networks and mixed integer linear programming. In this paper, we design a new method for inferring a polymer based on the framework. For this, we introduce a new way of representing a polymer as a form of monomer and define new descriptors that feature the structure of polymers. We also use linear regression as a building block of constructing a prediction function in the framework. The results of our computational experiments reveal a set of chemical properties on polymers to which a prediction function constructed with linear regression performs well. We also observe that the proposed method can infer polymers with up to 50 non-hydrogen atoms in a monomer form.

cs.LG↗

arXiv2021

An Inverse QSAR Method Based on Linear Regression and Integer Programming

Recently a novel framework has been proposed for designing the molecular structure of chemical compounds using both artificial neural networks (ANNs) and mixed integer linear programming (MILP). In the framework, we first define a feature vector $f(C)$ of a chemical graph $C$ and construct an ANN that maps $x=f(C)$ to a predicted value $η(x)$ of a chemical property $π$ to $C$. After this, we formulate an MILP that simulates the computation process of $f(C)$ from $C$ and that of $η(x)$ from $x$. Given a target value $y^*$ of the chemical property $π$, we infer a chemical graph $C^\dagger$ such that $η(f(C^\dagger))=y^*$ by solving the MILP. In this paper, we use linear regression to construct a prediction function $η$ instead of ANNs. For this, we derive an MILP formulation that simulates the computation process of a prediction function by linear regression. The results of computational experiments suggest our method can infer chemical graphs with around up to 50 non-hydrogen atoms.

cs.LG↗

arXiv2021

Molecular Design Based on Artificial Neural Networks, Integer Programming and Grid Neighbor Search

A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property using both artificial neural networks and mixed integer linear programming. In the framework, a chemical graph with a target chemical value is inferred as a feasible solution of a mixed integer linear program that represents a prediction function and other requirements on the structure of graphs. In this paper, we propose a procedure for generating other feasible solutions of the mixed integer linear program by searching the neighbor of output chemical graph in a search space. The procedure is combined in the framework as a new building block. The results of our computational experiments suggest that the proposed method can generate an additional number of new chemical graphs with up to 50 non-hydrogen atoms.

cs.LG↗

arXiv2021

Recycling Solutions for Vertex Coloring Heuristics

The vertex coloring problem is a well-known NP-hard problem and has many applications in operations research and in scheduling. A conventional approach to the problem solves the k-colorability problem iteratively, decreasing k one by one. Whether a heuristic algorithm finds a legal k-coloring quickly or not is largely affected by an initial solution. We highlight a simple initial solution generator, which we call the recycle method, which makes use of the legal (k+1)-coloring that has been found. An initial solution generated by the method is expected to guide a heuristic algorithm to find a legal k-coloring more quickly than conventional methods, as demonstrated by experimental studies. The results suggest that the recycle method should be used as the standard initial solution generator for both local search algorithms and modern hybrid methods.

cs.DM↗