arXiv subjects

Yixin Cao

Publications and source records attributed to Yixin Cao.

At least 181 records · Page 10Linked to original sources

arXiv2018

Structural and Topological Nature of Plasticity in Sheared Granular Materials

Upon mechanical loading, granular materials yield and undergo plastic deformation. The nature of plastic deformation is essential for the development of the macroscopic constitutive models and the understanding of shear band formation. However, we still do not fully understand the microscopic nature of plastic deformation in disordered granular materials. Here we used synchrotron X-ray tomography technique to track the structural evolutions of three-dimensional granular materials under shear. We establish that highly distorted coplanar tetrahedra are the structural defects responsible for microscopic plasticity in disordered granular packings. The elementary plastic events occur through flip events which correspond to a neighbor switching process among these coplanar tetrahedra (or equivalently as the rotation motion of 4-ring disclinations). These events are discrete in space and possess specific orientations with the principal stress direction.

cond-mat.soft↗

arXiv2018

A Polynomial Kernel for Diamond-Free Editing

An $H$-free editing problem asks whether we can edit at most $k$ edges to make a graph contain no induced copy of the fixed graph $H$. We obtain a polynomial kernel for this problem when $H$ is a diamond. The incompressibility dichotomy for $H$ being a 3-connected graph and the classical complexity dichotomy suggest that except for $H$ being a complete/empty graph, $H$-free editing problems admit polynomial kernels only for a few small graphs $H$. Therefore, we believe that our result is an essential step toward a complete dichotomy on the compressibility of $H$-free editing. Additionally, we give a cubic-vertex kernel for the diamond-free edge deletion problem, which is far simpler than the previous kernel of the same size for the problem.

cs.DS↗

arXiv2018

Translational and rotational dynamical heterogeneities in granular systems

We use X-ray tomography to investigate the translational and rotational dynamical heterogeneities of a three dimensional hard ellipsoids granular packing driven by oscillatory shear. We find that particles which translate quickly form clusters with a size distribution given by a power-law with an exponent that is independent of the strain amplitude. Identical behavior is found for particles that are translating slowly, rotating quickly, or rotating slowly. The geometrical properties of these four different types of clusters are the same as those of random clusters. Different cluster types are considerably correlated/anticorrelated, indicating a significant coupling between translational and rotational degrees of freedom. Surprisingly these clusters are formed already at time scales that are much shorter than the $α-$relaxation time, in stark contrast to the behavior found in glass-forming systems.

cond-mat.dis-nn↗

arXiv2018

Visually Explainable Recommendation

Images account for a significant part of user decisions in many application scenarios, such as product images in e-commerce, or user image posts in social networks. It is intuitive that user preferences on the visual patterns of image (e.g., hue, texture, color, etc) can be highly personalized, and this provides us with highly discriminative features to make personalized recommendations. Previous work that takes advantage of images for recommendation usually transforms the images into latent representation vectors, which are adopted by a recommendation component to assist personalized user/item profiling and recommendation. However, such vectors are hardly useful in terms of providing visual explanations to users about why a particular item is recommended, and thus weakens the explainability of recommendation systems. As a step towards explainable recommendation models, we propose visually explainable recommendation based on attentive neural networks to model the user attention on images, under the supervision of both implicit feedback and textual reviews. By this, we can not only provide recommendation results to the users, but also tell the users why an item is recommended by providing intuitive visual highlights in a personalized manner. Experimental results show that our models are not only able to improve the recommendation performance, but also can provide persuasive visual explanations for the users to take the recommendations.

cs.IR↗

arXiv2017

An $O^*(1.84^k)$ Parameterized Algorithm for the Multiterminal Cut Problem

We study the \emph{multiterminal cut} problem, which, given an $n$-vertex graph whose edges are integer-weighted and a set of terminals, asks for a partition of the vertex set such that each terminal is in a distinct part, and the total weight of crossing edges is at most $k$. Our weapons shall be two classical results known for decades: \emph{maximum volume minimum ($s,t$)-cuts} by [Ford and Fulkerson, \emph{Flows in Networks}, 1962] and \emph{isolating cuts} by [Dahlhaus et al., \emph{SIAM J. Comp.} 23(4):864-894, 1994]. We sharpen these old weapons with the help of submodular functions, and apply them to this problem, which enable us to design a more elaborated branching scheme on deciding whether a non-terminal vertex is with a terminal or not. This bounded search tree algorithm can be shown to run in $1.84^k\cdot n^{O(1)}$ time, thereby breaking the $2^k\cdot n^{O(1)}$ barrier. As a by-product, it gives a $1.36^k\cdot n^{O(1)}$ time algorithm for $3$-terminal cut. The preprocessing applied on non-terminal vertices might be of use for study of this problem from other aspects.

cs.DS↗

arXiv2017

Granular materials flow like complex fluids

Granular materials such as sand, powders, foams etc. are ubiquitous in our daily life, as well as in industrial and geotechnical applications. Although these disordered systems form stable structures if unperturbed, in practice they do relax because of the presence of unavoidable external influences such as tapping or shear. Often it is tacitly assumed that for granular systems this relaxation dynamics is similar to the one of thermal glass-formers, but in fact experimental difficulties have so far prevented to determine the dynamic properties of three dimensional granular systems on the particle level. This lack of experimental data, combined with the fact that in these systems the motion of the particles involves friction, makes it very challenging to come up with an accurate description of their relaxation dynamics. Here we use X-ray tomography to determine the microscopic relaxation dynamics of hard granular ellipsoids that are subject to an oscillatory shear. We find that the distribution function of the particle displacement can be described by a Gumbel law with a shape parameter that is independent of time and the strain amplitude $γ$. Despite this universality, the mean squared displacement of a tagged particle shows power-laws as a function of time with an exponent that depends on $γ$ and the time interval considered. We argue that these results are directly related to the existence of the microscopic relaxation mechanisms that involve friction and memory effects. These observations demonstrate that on the particle level the dynamical behavior of granular systems is qualitatively different from the one of thermal glass-formers and instead more similar to the one of complex fluids. Thus we conclude that granular materials can relax even when the driving is weak, an insight which impacts our understanding of the nature of granular solids.

cond-mat.soft↗

arXiv2017

A Naive Algorithm for Feedback Vertex Set

Given a graph on $n$ vertices and an integer $k$, the feedback vertex set problem asks for the deletion of at most $k$ vertices to make the graph acyclic. We show that a greedy branching algorithm, which always branches on an undecided vertex with the largest degree, runs in single-exponential time, i.e., $O(c^k\cdot n^2)$ for some constant $c$.

cs.DS↗

arXiv2017

Vertex Deletion Problems on Chordal Graphs

Containing many classic optimization problems, the family of vertex deletion problems has an important position in algorithm and complexity study. The celebrated result of Lewis and Yannakakis gives a complete dichotomy of their complexity. It however has nothing to say about the case when the input graph is also special. This paper initiates a systematic study of vertex deletion problems from one subclass of chordal graphs to another. We give polynomial-time algorithms or proofs of NP-completeness for most of the problems. In particular, we show that the vertex deletion problem from chordal graphs to interval graphs is NP-complete.

cs.DS↗

arXiv2017

Origin of Non-cubic Scaling Law in Disordered Granular Packing

Recent diffraction experiments on metallic glasses have unveiled an unexpected non-cubic scaling law between density and average interatomic distance, which lead to the speculations on the presence of fractal glass order. Using X-ray tomography we identify here a similar non-cubic scaling law in disordered granular packing of spherical particles. We find that the scaling law is directly related to the contact neighbors within first nearest neighbor shell, and therefore is closely connected to the phenomenon of jamming. The seemingly universal scaling exponent around 2.5 arises due to the isostatic condition with contact number around 6, and we argue that the exponent should not be universal.

cond-mat.soft↗

arXiv2016

Unit Interval Editing is Fixed-Parameter Tractable

Given a graph~$G$ and integers $k_1$, $k_2$, and~$k_3$, the unit interval editing problem asks whether $G$ can be transformed into a unit interval graph by at most $k_1$ vertex deletions, $k_2$ edge deletions, and $k_3$ edge additions. We give an algorithm solving this problem in time $2^{O(k\log k)}\cdot (n+m)$, where $k := k_1 + k_2 + k_3$, and $n, m$ denote respectively the numbers of vertices and edges of $G$. Therefore, it is fixed-parameter tractable parameterized by the total number of allowed operations. Our algorithm implies the fixed-parameter tractability of the unit interval edge deletion problem, for which we also present a more efficient algorithm running in time $O(4^k \cdot (n + m))$. Another result is an $O(6^k \cdot (n + m))$-time algorithm for the unit interval vertex deletion problem, significantly improving the algorithm of van 't Hof and Villanger, which runs in time $O(6^k \cdot n^6)$.

cs.DS↗

arXiv2016

Unit Interval Vertex Deletion: Fewer Vertices are Relevant

The unit interval vertex deletion problem asks for a set of at most $k$ vertices whose deletion from an $n$-vertex graph makes it a unit interval graph. We develop an $O(k^4)$-vertex kernel for the problem, significantly improving the $O(k^{53})$-vertex kernel of Fomin, Saurabh, and Villanger [ESA'12; SIAM J. Discrete Math 27(2013)]. We introduce a novel way of organizing cliques of a unit interval graph. Our constructive proof for the correctness of our algorithm, using interval models, greatly simplifies the destructive proofs, based on forbidden induced subgraphs, for similar problems in literature.

cs.DS↗

arXiv2016

Minimum Fill-In: Inapproximability and Almost Tight Lower Bounds

Given an $n*n$ sparse symmetric matrix with $m$ nonzero entries, performing Gaussian elimination may turn some zeroes into nonzero values. To maintain the matrix sparse, we would like to minimize the number $k$ of these changes, hence called the minimum fill-in problem. Agrawal et al.~[FOCS'90] developed the first approximation algorithm, based on early heuristics by George [SIAM J Numer Anal 10] and by Lipton et al.~[SIAM J Numer Anal 16]. The objective function they used is $m+k$, the number of nonzero elements after elimination. An approximation algorithm using $k$ as the objective function was presented by Natanzon et al.~[STOC'98]. These two versions are incomparable in terms of approximation. Parameterized algorithms for the problem was first studied by Kaplan et al.~[FOCS'94]. Fomin & Villanger [SODA'12] recently gave an algorithm running in time $2^{O(\sqrt{k} \log k)}+n^{O(1)}$. Hardness results of this problem are surprisingly scarce, and the few known ones are either weak or have to use nonstandard complexity conjectures. The only inapproximability result by Wu et al.~[IJCAI'15] applies to only the objective function $m+k$, and is grounded on the Small Set Expansion Conjecture. The only nontrivial parameterized lower bounds, by Bliznets et al.~[SODA'16], include a very weak one based on ETH, and a strong one based on hardness of subexponential-time approximation of the minimum bisection problem on regular graphs. For both versions of the problem, we exclude the existence of PTASs, assuming P$\ne$NP, and the existence of $2^{O(n^{1-δ})}$-time approximation schemes for any positive $δ$, assuming ETH. It also implies a $2^{O(k^{1/2-δ})} n^{O(1)}$ parameterized lower bound. Behind these results is a new reduction from vertex cover, which might be of its own interest: All previous reductions for similar problems are from some kind of graph layout problems.

cs.CC↗

arXiv2015

Approximate Association via Dissociation

A vertex set $X$ of a graph $G$ is an association set if each component of $G - X$ is a clique, or a dissociation set if each component of $G - X$ is a single vertex or a single edge. Interestingly, $G - X$ is then precisely a graph containing no induced $P_3$'s or containing no $P_3$'s, respectively. We observe some special structures and show that if none of them exists, then the minimum association set problem can be reduced to the minimum (weighted) dissociation set problem. This yields the first nontrivial approximation algorithm for association set, and its approximation ratio is 2.5, matching the best result of the closely related cluster editing problem. The reduction is based on a combinatorial study of modular decomposition of graphs free of these special structures. Further, a novel algorithmic use of modular decomposition enables us to implement this approach in $O(m n + n^2)$ time.

cs.DS↗

arXiv2015

The structural origin of the hard-sphere glass transition in granular packing

Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a "hidden" polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. Our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.

cond-mat.soft↗

arXiv2014

A $2k$-Vertex Kernel for Maximum Internal Spanning Tree

We consider the parameterized version of the maximum internal spanning tree problem, which, given an $n$-vertex graph and a parameter $k$, asks for a spanning tree with at least $k$ internal vertices. Fomin et al. [J. Comput. System Sci., 79:1-6] crafted a very ingenious reduction rule, and showed that a simple application of this rule is sufficient to yield a $3k$-vertex kernel. Here we propose a novel way to use the same reduction rule, resulting in an improved $2k$-vertex kernel. Our algorithm applies first a greedy procedure consisting of a sequence of local exchange operations, which ends with a local-optimal spanning tree, and then uses this special tree to find a reducible structure. As a corollary of our kernel, we obtain a deterministic algorithm for the problem running in time $4^k \cdot n^{O(1)}$.

cs.DS↗

arXiv2014

Linear Recognition of Almost Interval Graphs

Let $\mbox{interval} + k v$, $\mbox{interval} + k e$, and $\mbox{interval} - k e$ denote the classes of graphs that can be obtained from some interval graph by adding $k$ vertices, adding $k$ edges, and deleting $k$ edges, respectively. When $k$ is small, these graph classes are called almost interval graphs. They are well motivated from computational biology, where the data ought to be represented by an interval graph while we can only expect an almost interval graph for the best. For any fixed $k$, we give linear-time algorithms for recognizing all these classes, and in the case of membership, our algorithms provide also a specific interval graph as evidence. When $k$ is part of the input, these problems are also known as graph modification problems, all NP-complete. Our results imply that they are fixed-parameter tractable parameterized by $k$, thereby resolving the long-standing open problem on the parameterized complexity of recognizing $\mbox{interval}+ k e$, first asked by Bodlaender et al. [Bioinformatics, 11:49--57, 1995]. Moreover, our algorithms for recognizing $\mbox{interval}+ k v$ and $\mbox{interval}- k e$ run in times $O(6^k \cdot (n + m))$ and $O(8^k \cdot (n + m))$, (where $n$ and $m$ stand for the numbers of vertices and edges respectively in the input graph,) significantly improving the $O(k^{2k}\cdot n^3m)$-time algorithm of Heggernes et al. [STOC 2007] and the $O(10^k \cdot n^9)$-time algorithm of Cao and Marx [SODA 2014] respectively.

cs.DM↗

arXiv2014

On Feedback Vertex Set: New Measure and New Structures

We present a new parameterized algorithm for the {feedback vertex set} problem ({\sc fvs}) on undirected graphs. We approach the problem by considering a variation of it, the {disjoint feedback vertex set} problem ({\sc disjoint-fvs}), which finds a feedback vertex set of size $k$ that has no overlap with a given feedback vertex set $F$ of the graph $G$. We develop an improved kernelization algorithm for {\sc disjoint-fvs} and show that {\sc disjoint-fvs} can be solved in polynomial time when all vertices in $G \setminus F$ have degrees upper bounded by three. We then propose a new branch-and-search process on {\sc disjoint-fvs}, and introduce a new branch-and-search measure. The process effectively reduces a given graph to a graph on which {\sc disjoint-fvs} becomes polynomial-time solvable, and the new measure more accurately evaluates the efficiency of the process. These algorithmic and combinatorial studies enable us to develop an $O^*(3.83^k)$-time parameterized algorithm for the general {\sc fvs} problem, improving all previous algorithms for the problem.

cs.DS↗

arXiv2014

Chordal Editing is Fixed-Parameter Tractable

Graph modification problems are typically asked as follows: is there a small set of operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and edge addition; for the same property, one can define significantly different versions by allowing different operations. We study a very general graph modification problem which allows all three types of operations: given a graph $G$ and integers $k_1$, $k_2$, and $k_3$, the \textsc{chordal editing} problem asks whether $G$ can be transformed into a chordal graph by at most $k_1$ vertex deletions, $k_2$ edge deletions, and $k_3$ edge additions. Clearly, this problem generalizes both \textsc{chordal vertex/edge deletion} and \textsc{chordal completion} (also known as \textsc{minimum fill-in}). Our main result is an algorithm for \textsc{chordal editing} in time $2^{O(k\log k)}\cdot n^{O(1)}$, where $k:=k_1+k_2+k_3$ and $n$ is the number of vertices of $G$. Therefore, the problem is fixed-parameter tractable parameterized by the total number of allowed operations. Our algorithm is both more efficient and conceptually simpler than the previously known algorithm for the special case \textsc{chordal deletion}.

cs.DS↗