arXiv subjects

Akira Suzuki

Publications and source records attributed to Akira Suzuki.

At least 37 records · Page 2Linked to original sources

arXiv2019

Trichotomy for the reconfiguration problem of integer linear systems

In this paper, we consider the reconfiguration problem of integer linear systems. In this problem, we are given an integer linear system $I$ and two feasible solutions $\boldsymbol{s}$ and $\boldsymbol{t}$ of $I$, and then asked to transform $\boldsymbol{s}$ to $\boldsymbol{t}$ by changing a value of only one variable at a time, while maintaining a feasible solution of $I$ throughout. $Z(I)$ for $I$ is the complexity index introduced by Kimura and Makino (Discrete Applied Mathematics 200:67--78, 2016), which is defined by the sign pattern of the input matrix. We analyze the complexity of the reconfiguration problem of integer linear systems based on the complexity index $Z(I)$ of given $I$. We then show that the problem is (i) solvable in constant time if $Z(I)$ is less than one, (ii) weakly coNP-complete and pseudo-polynomially solvable if $Z(I)$ is exactly one, and (iii) PSPACE-complete if $Z(I)$ is greater than one. Since the complexity indices of Horn and two-variable-par-inequality integer linear systems are at most one, our results imply that the reconfiguration of these systems are in coNP and pseudo-polynomially solvable. Moreover, this is the first result that reveals coNP-completeness for a reconfiguration problem, to the best of our knowledge.

cs.DS↗

arXiv2018

Incremental Optimization of Independent Sets under Reachability Constraints

We introduce a new framework for reconfiguration problems, and apply it to independent sets as the first example. Suppose that we are given an independent set $I_0$ of a graph $G$, and an integer $l \ge 0$ which represents a lower bound on the size of any independent set of $G$. Then, we are asked to find an independent set of $G$ having the maximum size among independent sets that are reachable from $I_0$ by either adding or removing a single vertex at a time such that all intermediate independent sets are of size at least $l$. We show that this problem is PSPACE-hard even for bounded pathwidth graphs, and remains NP-hard for planar graphs. On the other hand, we give a linear-time algorithm to solve the problem for chordal graphs. We also study the fixed-parameter (in)tractability of the problem with respect to the following three parameters: the degeneracy $d$ of an input graph, a lower bound $l$ on the size of the independent sets, and a lower bound $s$ on the solution size. We show that the problem is fixed-parameter intractable when only one of $d$, $l$, and $s$ is taken as a parameter. On the other hand, we give a fixed-parameter algorithm when parameterized by $s+d$; this result implies that the problem parameterized only by $s$ is fixed-parameter tractable for planar graphs, and for bounded treewidth graphs.

cs.DM↗

arXiv2018

Reconfiguring spanning and induced subgraphs

Subgraph reconfiguration is a family of problems focusing on the reachability of the solution space in which feasible solutions are subgraphs, represented either as sets of vertices or sets of edges, satisfying a prescribed graph structure property. Although there has been previous work that can be categorized as subgraph reconfiguration, most of the related results appear under the name of the property under consideration; for example, independent set, clique, and matching. In this paper, we systematically clarify the complexity status of subgraph reconfiguration with respect to graph structure properties.

cs.DS↗

arXiv2016

The Complexity of (List) Edge-Coloring Reconfiguration Problem

Let $G$ be a graph such that each edge has its list of available colors, and assume that each list is a subset of the common set consisting of $k$ colors. Suppose that we are given two list edge-colorings $f_0$ and $f_r$ of $G$, and asked whether there exists a sequence of list edge-colorings of $G$ between $f_0$ and $f_r$ such that each list edge-coloring can be obtained from the previous one by changing a color assignment of exactly one edge. This problem is known to be PSPACE-complete for every integer $k \ge 6$ and planar graphs of maximum degree three, but any complexity hardness was unknown for the non-list variant. In this paper, we first improve the known result by proving that, for every integer $k \ge 4$, the problem remains PSPACE-complete even if an input graph is planar, bounded bandwidth, and of maximum degree three. We then give the first complexity hardness result for the non-list variant: for every integer $k \ge 5$, we prove that the non-list variant is PSPACE-complete even if an input graph is planar, of bandwidth linear in $k$, and of maximum degree $k$.

cs.DM↗

arXiv2016

Theory of the Room-Temperature QHE in Graphene

The unusual quantum Hall effect (QHE) in graphene is often discussed in terms of Dirac fermions moving with a linear dispersion relation. The same phenomenon will be explained in terms of the more traditional composite bosons, which move with a linear dispersion relation. The "electron" (wave packet) moves easier in the direction [1,1,0,c-axis] = [1,1,0] of the honeycomb lattice than perpendicular to it, while the "hole" moves easier in [0,0,1]. Since "electrons" and "holes" move in different channels, the number densities can be high especially when the Fermi surface has "necks". The strong QHE arises from the phonon exchange attraction in the neighborhood of the "neck" Fermi surfaces. The plateau observed for the Hall conductivity and the accompanied resistivity drop is due to the Bose-Einstein condensation of the c-bosons, each forming from a pair of one-electron--two-fluxons c-fermions by phonon-exchange attraction.

cond-mat.supr-con↗

arXiv2015

Identities for Entropy Change Associated with the Time-Evolution of an Open System

A general relation between entropy and an evolutionary superoperator is derived based on the theory of the real-time formulation. The formulation establishing the relation relies only on the framework of quantum statistical mechanics and the standard definition of the von Neumann entropy. Applying the theory of the imaginary-time formulation, a similar relation is obtained for the entropy change due to the change in reservoir temperatures. To show the usefulness of these formulas, we derived the expression for the entropy production induced by some dissipation in an open quantum system as the exemplary model system.

cond-mat.stat-mech↗

arXiv2015

The complexity of dominating set reconfiguration

Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such that each dominating set in the sequence is of cardinality at most $k$ and can be obtained from the previous one by either adding or deleting exactly one vertex. This problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this decision problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, trees, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence such that the number of additions and deletions is bounded by $O(n)$, where $n$ is the number of vertices in the input graph.

cs.DM↗

arXiv2014

Computational Complexity of Competitive Diffusion on (Un)weighted Graphs

Consider an undirected graph modeling a social network, where the vertices represent users, and the edges do connections among them. In the competitive diffusion game, each of a number of players chooses a vertex as a seed to propagate his/her opinion, and then it spreads along the edges in the graphs. The objective of every player is to maximize the number of vertices the opinion infects. In this paper, we investigate a computational problem of asking whether a pure Nash equilibrium exists in the competitive diffusion game on unweighed and weighted graphs, and present several negative and positive results. We first prove that the problem is W[1]-hard when parameterized by the number of players even for unweighted graphs. We also show that the problem is NP-hard even for series-parallel graphs with positive integer weights, and is NP-hard even for forests with arbitrary integer weights. Furthermore, we show that the problem for forest of paths with arbitrary weights is solvable in pseudo-polynomial time; and it is solvable in quadratic time if a given graph is unweighted. We also prove that the problem for chain, cochain, and threshold graphs with arbitrary integer weights is solvable in polynomial time.

cs.CC↗

arXiv2014

Reconfiguration of Dominating Sets

We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph $G$ is a set $S$ of vertices such that each vertex is either in $S$ or has a neighbour in $S$. In a reconfiguration problem, the goal is to determine whether there exists a sequence of feasible solutions connecting given feasible solutions $s$ and $t$ such that each pair of consecutive solutions is adjacent according to a specified adjacency relation. Two dominating sets are adjacent if one can be formed from the other by the addition or deletion of a single vertex. For various values of $k$, we consider properties of $D_k(G)$, the graph consisting of a vertex for each dominating set of size at most $k$ and edges specified by the adjacency relation. Addressing an open question posed by Haas and Seyffarth, we demonstrate that $D_{Γ(G)+1}(G)$ is not necessarily connected, for $Γ(G)$ the maximum cardinality of a minimal dominating set in $G$. The result holds even when graphs are constrained to be planar, of bounded tree-width, or $b$-partite for $b \ge 3$. Moreover, we construct an infinite family of graphs such that $D_{γ(G)+1}(G)$ has exponential diameter, for $γ(G)$ the minimum size of a dominating set. On the positive side, we show that $D_{n-m}(G)$ is connected and of linear diameter for any graph $G$ on $n$ vertices having at least $m+1$ independent edges.

cs.DM↗

arXiv2013

On the Parameterized Complexity of Reconfiguration Problems

We present the first results on the parameterized complexity of reconfiguration problems, where a reconfiguration version of an optimization problem $Q$ takes as input two feasible solutions $S$ and $T$ and determines if there is a sequence of {\em reconfiguration steps} that can be applied to transform $S$ into $T$ such that each step results in a feasible solution to $Q$. For most of the results in this paper, $S$ and $T$ are subsets of vertices of a given graph and a reconfiguration step adds or deletes a vertex. Our study is motivated by recent results establishing that for most NP-hard problems, the classical complexity of reconfiguration is PSPACE-complete. We address the question for several important graph properties under two natural parameterizations: $k$, the size of the solutions, and $\ell$, the length of the sequence of steps. Our first general result is an algorithmic paradigm, the {\em reconfiguration kernel}, used to obtain fixed-parameter algorithms for the reconfiguration versions of {\sc Vertex Cover} and, more generally, {\sc Bounded Hitting Set} and {\sc Feedback Vertex Set}, all parameterized by $k$. In contrast, we show that reconfiguring {\sc Unbounded Hitting Set} is $W[2]$-hard when parameterized by $k+\ell$. We also demonstrate the $W[1]$-hardness of the reconfiguration versions of a large class of maximization problems parameterized by $k+\ell$, and of their corresponding deletion problems parameterized by $\ell$; in doing so, we show that there exist problems in FPT when parameterized by $k$, but whose reconfiguration versions are $W[1]$-hard when parameterized by $k+\ell$.

cs.CC↗

arXiv2013

Statistical mechanical expression of entropy production for an open quantum system

A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in quantum mechanics. The general relation between system-reservoir interactions and an entropy change operator in an open quantum system, relying just on the framework of statistical mechanics and the definition of von Neumann entropy. By using this formula, we can obtain the correct entropy production in the linear response framework. The present derivation of entropy production is directly based on the first principle of microscopic time-evolution, while the previous standard argument is due to the thermodynamic energy balance.

cond-mat.stat-mech↗

arXiv2013

Composite-particles (Boson, Fermion) Theory of Fractional Quantum Hall Effect

A quantum statistical theory is developed for a fractional quantum Hall effects in terms of composite bosons (fermions) each of which contains a conduction electron and an odd (even) number of fluxons. The cause of the QHE is by assumption the phonon exchange attraction between the conduction electron ("electron", "hole") and fluxons (quanta of magnetic fluxes). We postulate that c-fermions with \emph{any} even number of fluxons have an effective charge (magnitude) equal to the electron charge $e$. The density of c-fermions with $m$ fluxons, $n_ϕ^{(m)}$, is connected with the electron density $n_{\mathrm e}$ by $n_ϕ^{(m)}=n_{\mathrm e}/m$, which implies a more difficult formation for higher $m$, generating correct values $me^2/h$ for the Hall conductivity $σ_{\mathrm H}\equiv j/E_{\mathrm H}$. For condensed c-bosons the density of c-bosons-with-$m$ fluxons, $n_ϕ^{(m)}$, is connected with the boson density $n_0$ by $n_ϕ^{(m)}=n_0/m$. This yields $σ_{\mathrm H}=m\,e^2/h$ for the magnetoconductivity, the value observed of the QHE at filling factor $ν=1/m$ ($m=$odd numbers). Laughlin's theory and results about the fractional charge are not borrowed in the present work.

cond-mat.mes-hall↗

arXiv2012

On the metal-insulator-transition in vanadium dioxide

Vanadium dioxide (VO$_2$) undergoes a metal-insulator transition (MIT) at 340 K with the structural change between tetragonal and monoclinic crystals as the temperature is lowered. The conductivity $σ$ drops at MIT by four orders of magnitude. The low-temperature monoclinic phase is known to have a lower ground-state energy. The existence of a $k$-vector ${\boldsymbol k}$ is prerequisite for the conduction since the ${\boldsymbol k}$ appears in the semiclassical equation of motion for the conduction electron (wave packet). Each wave packet is, by assumption, composed of the plane waves proceeding in the ${\boldsymbol k}$ direction perpendicular to the plane. The tetragonal (VO$_2$)$_3$ unit cells are periodic along the crystal's $x$-, $y$-, and z-axes, and hence there are three-dimensional $k$-vectors. The periodicity using the non-orthogonal bases does not legitimize the electron dynamics in solids. There are one-dimensional ${\boldsymbol k}$ along the c-axis for a monoclinic crystal. We believe this decrease in the dimensionality of the $k$-vectors is the cause of the conductivity drop. Triclinic and trigonal (rhombohedral) crystals have no $k$-vectors, and hence they must be insulators. The majority carriers in graphite are "electrons", which is shown by using an orthogonal unit cell for the hexagonal lattice.

cond-mat.mtrl-sci↗

arXiv2009

The two-atom energy spectrum in a harmonic trap near a Feshbach resonance at higher partial waves

Two atoms in an optical lattice may be made to interact strongly at higher partial waves near a Feshbach resonance. These atoms, under appropriate constraints, could be bosonic or fermionic. The universal $l=2$ energy spectrum for such a system, with a caveat, is presented in this paper, and checked with the spectrum obtained by direct numerical integration of the Schrödinger equation. The results reported here extend those of Yip for p-wave resonance (Phys. Rev. A {\bf 78}, 013612 (2008)), while exploring the limitations of a universal expression for the spectrum for the higher partial waves.

cond-mat.quant-gas↗

arXiv2006

P-Wave Charmed-Strange Mesons

We examine charmed-strange mesons within the framework of the constituent quark model, focusing on the states with L=1. We are particularly interested in the mixing of two spin-states that are involved in $D_{s1}(2536)$ and the recently discovered $D_{sJ}(2460)$. We assume that these two mesons form a pair of states with J=1. These spin-states are mixed by a type of the spin-orbit interaction that violates the total-spin conservation. Without assuming explicit forms for the interactions as functions of the interquark distance, we relate the matrix elements of all relevant spin-dependent interactions to the mixing angle and the observed masses of the L=1 quartet. We find that the spin-spin interaction, among various types of the spin-dependent interactions, plays a particularly interesting role in determining the spin structure of $D_{s1}(2536)$ and $D_{sJ}(2460)$.

hep-ph↗

arXiv2004

Shape invariant potentials in SUSY quantum mechanics and periodic orbit theory

We examine shape invariant potentials (excluding those that are obtained by scaling) in supersymmetric quantum mechanics from the stand-point of periodic orbit theory. An exact trace formula for the quantum spectra of such potentials is derived. Based on this result, and Barclay's functional relationship for such potentials, we present a new derivation of the result that the lowest order SWKB quantisation rule is exact.

quant-ph↗

arXiv2002

Some exact results for a trapped quantum gas at finite temperature

We present closed analytical expressions for the particle and kinetic energy spatial densities at finite temperatures for a system of noninteracting fermions (bosons) trapped in a d-dimensional harmonic oscillator potential. For d=2 and 3, exact expressions for the N-particle densities are used to calculate perturbatively the temperature dependence of the splittings of the energy levels in a given shell due to a very weak interparticle interaction in a dilute Fermi gas. In two dimensions, we obtain analytically the surprising result that the |l|-degeneracy in a harmonic oscillator shell is not lifted in the lowest order even when the exact, rather than the Thomas-Fermi expression for the particle density is used. We also demonstrate rigorously (in two dimensions) the reduction of the exact zero-temperature fermionic expressions to the Thomas-Fermi form in the large-N limit.

cond-mat.stat-mech↗

arXiv1995

Quantum Solitons in the Calogero-Sutherland Model

We show that the single quasi-particle Schrödinger equation for a certain form of one-body potential yields a stationary one soliton solution. The one-body potential is assumed to arise from the self- interacting charge distribution with the singular kernel of the Calogero-Sutherland model. The quasi-particle has negative or positive charge for negative or positive coupling constant of the interaction. The magnitude of the charge is unity only for the semion. It is also pointed out that for repulsive coupling, our equation is mathematically the same as the steady-state Smoluchowski equation of Dyson's Coulomb gas model.

cond-mat↗