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On the Structural Properties of Social Networks and their Measurement-calibrated Synthetic CounterpartsAug 22 2019Data-driven analysis of large social networks has attracted a great deal of research interest. In this paper, we investigate 120 real social networks and their measurement-calibrated synthetic counterparts generated by four well-known network models. ... More
The agreement distance of unrooted phylogenetic networksAug 22 2019A rearrangement operation makes a small graph-theoretical change to a phylogenetic network to transform it into another one. For unrooted phylogenetic trees and networks, popular rearrangement operations are tree bisection and reconnection (TBR) and prune ... More
Line and Plane Cover Numbers RevisitedAug 20 2019A measure for the visual complexity of a straight-line crossing-free drawing of a graph is the minimum number of lines needed to cover all vertices. For a given graph $G$, the minimum such number (over all drawings in dimension $d \in \{2,3\}$) is called ... More
Noisy Corruption DetectionAug 20 2019We answer a question of Alon, Mossel, and Pemantle about the corruption detection model on graphs in the noisy setting.
An Omega(n^2) Lower Bound for Random Universal Sets for Planar GraphsAug 19 2019A set $U\subseteq \reals^2$ is $n$-universal if all $n$-vertex planar graphs have a planar straight-line embedding into $U$. We prove that if $Q \subseteq \reals^2$ consists of points chosen randomly and uniformly from the unit square then $Q$ must have ... More
Asymptotic degree distributions in random threshold graphsAug 19 2019We discuss several limiting degree distributions for a class of random threshold graphs in the many node regime. This analysis is carried out under a weak assumption on the distribution of the underlying fitness variable. This assumption, which is satisfied ... More
A Game of Cops and Robbers on Graphs with Periodic Edge-ConnectivityAug 19 2019This paper considers a game in which a single cop and a single robber take turns moving along the edges of a given graph $G$. If there exists a strategy for the cop which enables it to be positioned at the same vertex as the robber eventually, then $G$ ... More
Freezing, Bounded-Change and Convergent Cellular AutomataAug 19 2019This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes a bounded ... More
On bin packing with clustering and bin packing with delaysAug 19 2019We continue the study of two recently introduced bin packing type problems, called bin packing with clustering, and online bin packing with delays. A bin packing input consists of items of sizes not larger than 1, and the goal is to partition or pack ... More
Balanced Schnyder woods for planar triangulations: an experimental study with applications to graph drawing and graph separatorsAug 19 2019In this work we consider balanced Schnyder woods for planar graphs, which are Schnyder woods where the number of incoming edges of each color at each vertex is balanced as much as possible. We provide a simple linear-time heuristic leading to obtain well ... More
Safe sets in digraphsAug 19 2019A non-empty subset $S$ of the vertices of a digraph $D$ is called a {\it safe set} if \begin{itemize} \item[(i)] for every strongly connected component $M$ of $D-S$, there exists a strongly connected component $N$ of $D[S]$ such that there exists an arc ... More
On the edge-biclique graph and the iterated edge-biclique operatorAug 19 2019A biclique of a graph $G$ is a maximal induced complete bipartite subgraph of $G$. The edge-biclique graph of $G$, $KB_e(G)$, is the edge-intersection graph of the bicliques of $G$. A graph $G$ diverges (resp. converges or is periodic) under an operator ... More
Memory limitations are hidden in grammarAug 19 2019The ability to produce and understand an unlimited number of different sentences is a hallmark of human language. Linguists have sought to define the essence of this generative capacity using formal grammars that describe the syntactic dependencies between ... More
Energized simplicial complexesAug 19 2019For a simplicial complex with n sets, let W^-(x) be the set of sets in G contained in x and W^+(x) the set of sets in G containing x. An integer-valued function h on G defines for every A subset G an energy E[A]=sum_x in A h(x). The function energizes ... More
The stable set problem in graphs with bounded genus and bounded odd cycle packing numberAug 17 2019Consider the family of graphs without $ k $ node-disjoint odd cycles, where $ k $ is a constant. Determining the complexity of the stable set problem for such graphs $ G $ is a long-standing problem. We give a polynomial-time algorithm for the case that ... More
Finding Hamiltonian and Longest (s, t)-paths of C-shaped Supergrid Graphs in Linear TimeAug 17 2019A supergrid graph is a finite vertex-induced subgraph of the infinite graph whose vertex set consists of all points of the plane with integer coordinates and in which two vertices are adjacent if the difference of their x or y coordinates is not larger ... More
Discrete and Fast Fourier Transform Made ClearAug 17 2019Fast Fourier transform was included in the Top 10 Algorithms of 20th Century by Computing in Science & Engineering. In this paper, we provide a new simple derivation of both the discrete Fourier transform and fast Fourier transform by means of elementary ... More
Tracking Paths in Planar GraphsAug 15 2019We consider the NP-complete problem of tracking paths in a graph, first introduced by Banik et. al. [3]. Given an undirected graph with a source $s$ and a destination $t$, find the smallest subset of vertices whose intersection with any $s-t$ path results ... More
Connected Fair Allocation of Indivisible GoodsAug 15 2019We study the fair allocation of indivisible goods under the assumption that the goods form an undirected graph and each agent must receive a connected subgraph. Our focus is on well-studied fairness notions including envy-freeness and maximin share fairness. ... More
On Strict (Outer-)Confluent GraphsAug 14 2019A strict confluent (SC) graph drawing is a drawing of a graph with vertices as points in the plane, where vertex adjacencies are represented not by individual curves but rather by unique smooth paths through a planar system of junctions and arcs. If all ... More
The Power of the Weisfeiler-Leman Algorithm to Decompose GraphsAug 14 2019The Weisfeiler-Leman procedure is a widely-used approach for graph isomorphism testing that works by iteratively computing an isomorphism-invariant coloring of vertex tuples. Meanwhile, a fundamental tool in structural graph theory, which is often exploited ... More
Equitable partition of graphs into induced linear forestsAug 14 2019It is proved that the vertex set of any simple graph $G$ can be equitably partitioned into $k$ subsets for any integer $k\geq\max\{\big\lceil\frac{\Delta(G)+1}{2}\big\rceil,\big\lceil\frac{|G|}{4}\big\rceil\}$ so that each of them induces a linear forest. ... More
Light edges in 1-planar graphs of minimum degree 3Aug 14 2019A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one another edge. In this work we prove that each 1-planar graph of minimum degree at least $3$ contains an edge with degrees of its endvertices of type $(3,\leq23)$ ... More
Equitable tree-$O(d)$-coloring of $d$-degenerate graphsAug 14 2019An equitable tree-$k$-coloring of a graph is a vertex coloring on $k$ colors so that every color class incudes a forest and the sizes of any two color classes differ by at most one.This kind of coloring was first introduced in 2013 and can be used to ... More
Equitable vertex arboricity of $d$-degenerate graphsAug 14 2019A minimization problem in graph theory so-called the equitable tree-coloring problem can be used to formulate a structure decomposition problem on the communication network with some security considerations. Precisely, an equitable tree-$k$-coloring of ... More
Clustered Variants of Hajós' ConjectureAug 14 2019Haj\'os conjectured that every graph containing no subdivision of the complete graph $K_{s+1}$ is properly $s$-colorable. This result was disproved by Catlin. Indeed, the maximum chromatic number of such graphs is $\Omega(s^2/\log s)$. In this paper we ... More
3-choosable planar graphs with some precolored vertices and no $5^{-}$-cycles normally adjacent to $8^{-}$-cyclesAug 14 2019DP-coloring was introduced by Dvo\v{r}\'{a}k and Postle [J. Combin. Theory Ser. B 129 (2018) 38--54] as a generalization of list coloring. They used a "weak" version of DP-coloring to solve a longstanding conjecture by Borodin, stating that every planar ... More
Nonleaf Patterns in Trees: Protected Nodes and Fine NumbersAug 12 2019A closed-form formula is derived for the number of occurrences of matches of a multiset of patterns among all ordered (plane-planted) trees with a given number of edges. A pattern looks like a tree, with internal nodes and leaves, but also contain components ... More
A Natural Quadratic Approach to the Generalized Graph Layering ProblemAug 12 2019We propose a new exact approach to the generalized graph layering problem that is based on a particular quadratic assignment formulation. It expresses, in a natural way, the associated layout restrictions and several possible objectives, such as a minimum ... More
Bijective recurrences concerning two Schröder trianglesAug 11 2019Let $r(n,k)$ (resp. $s(n,k)$) be the number of Schr\"oder paths (resp. little Schr\"oder paths) of length $2n$ with $k$ hills, and set $r(0,0)=s(0,0)=1$. We bijectively establish the following recurrence relations: \begin{align*} r(n,0)&=\sum\limits_{j=0}^{n-1}2^{j}r(n-1,j), ... More
Avoidable paths in graphsAug 10 2019We prove a recent conjecture of Beisegel et al. that for every positive integer k, every graph containing an induced P_k also contains an avoidable P_k. Avoidability generalises the notion of simpliciality best known in the context of chordal graphs. ... More
High-girth near-Ramanujan graphs with localized eigenvectorsAug 10 2019We show that for every prime $d$ and $\alpha\in (0,1/6)$, there is an infinite sequence of $(d+1)$-regular graphs $G=(V,E)$ with girth at least $2\alpha \log_{d}(|V|)(1-o_d(1))$, second adjacency matrix eigenvalue bounded by $(3/\sqrt{2})\sqrt{d}$, and ... More
Crossing Numbers of Beyond-Planar GraphsAug 08 2019We study the 1-planar, quasi-planar, and fan-planar crossing number in comparison to the (unrestricted) crossing number of graphs. We prove that there are $n$-vertex 1-planar (quasi-planar, fan-planar) graphs such that any 1-planar (quasi-planar, fan-planar) ... More
Efficient Generation of Different Topological Representations of Graphs Beyond-PlanarityAug 08 2019Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings. Beside the study of a specific graph class for its ... More
A Note on Colourings of Connected Oriented Cubic GraphsAug 08 2019In this short note we show that every connected oriented cubic graph admits an 8-colouring. This lowers the best known upper bound for the chromatic number of connected oriented cubic graphs.
A Constraint Model for the Tree Decomposition of a GraphAug 07 2019We present a constraint model for the problem of producing a tree decomposition of a graph. The inputs to the model are a simple graph G, the number of nodes in the desired tree decomposition and the maximum cardinality of each node in that decomposition. ... More
A Universality Theorem for Nested PolytopesAug 06 2019In a nutshell, we show that polynomials and nested polytopes are topological, algebraic and algorithmically equivalent. Given two polytops $A\subseteq B$ and a number $k$, the Nested Polytope Problem (NPP) asks, if there exists a polytope $X$ on $k$ vertices ... More
On the maximum number of minimal connected dominating sets in convex bipartite graphsAug 06 2019The enumeration of minimal connected dominating sets is known to be notoriously hard for general graphs. Currently, it is only known that the sets can be enumerated slightly faster than $\mathcal{O}^{*}(2^n)$ and the algorithm is highly nontrivial. Moreover, ... More
Enumerating $k$-arc-connected orientationsAug 06 2019We give simple algorithms to enumerate the $\alpha$-orientations of a graph $G$ in delay $O(m^2)$ and to enumerate the outdegree sequences attained by $k$-arc-connected orientations of $G$ in delay $O(knm^2)$. Combining both yields an algorithm that enumerates ... More
Monotonic Representations of Outerplanar Graphs as Edge Intersection Graphs of Paths on a GridAug 06 2019A graph $G$ is called an edge intersection graph of paths on a grid if there is a grid and there is a set of paths on this grid, such that the vertices of $G$ correspond to the paths and two vertices of $G$ are adjacent if and only if the corresponding ... More
Recognizing and realizing cactus metricsAug 05 2019The problem of realizing finite metric spaces in terms of weighted graphs has many applications. For example, the mathematical and computational properties of metrics that can be realized by trees have been well-studied and such research has laid the ... More
Incorporating Structural Stigma into Network AnalysisAug 05 2019A rich literature has explored the modeling of homophily and other forms of nonuniform mixing associated with individual-level covariates within the exponential family random graph (ERGM) framework. Such differential mixing does not fully explain phenomena ... More
Faster algorithm for Cograph DeletionAug 03 2019In the Cograph Deletion problem the input is a graph $G$ and an integer $k$, and the goal is to decide whether there is a set of at most $k$ edges whose removal from $G$ results a graph that does not contain an induced path with four vertices. In this ... More
Finding Dominating Induced Matchings in $P_9$-Free Graphs in Polynomial TimeAug 02 2019Let $G=(V,E)$ be a finite undirected graph. An edge set $E' \subseteq E$ is a {\em dominating induced matching} ({\em d.i.m.}) in $G$ if every edge in $E$ is intersected by exactly one edge of $E'$. The \emph{Dominating Induced Matching} (\emph{DIM}) ... More
Independent Double Roman Domination on Block GraphsAug 02 2019Given a graph $G=(V,E)$, $f:V \rightarrow \{0,1,2 \}$ is the Italian dominating function of $G$ if $f$ satisfies $\sum_{u \in N(v)}f(u) \geq 2$ when $f(v)=0$. Denote $w(f)=\sum_{v \in V}f(v)$ as the weight of $f$. Let $V_i=\{v:f(v)=i\},i=0,1,2$, we call ... More
b-continuity and Partial Grundy Coloring of graphs with large girthAug 02 2019A b-coloring of a graph is a proper coloring such that each color class has at least one vertex which is adjacent to each other color class. The b-spectrum of $G$ is the set $S_{b}(G)$ of integers $k$ such that $G$ has a b-coloring with $k$ colors and ... More
On Cycle Transversals and Their Connected Variants in the Absence of a Small Linear ForestAug 01 2019A graph is $H$-free if it contains no induced subgraph isomorphic to $H$. We prove new complexity results for the two classical cycle transversal problems Feedback Vertex Set and Odd Cycle Transversal by showing that they can be solved in polynomial time ... More
An Improved Approximation Algorithm for TSP in the Half Integral CaseAug 01 2019We design a $1.49993$-approximation algorithm for the metric traveling salesperson problem (TSP) for instances in which an optimal solution to the subtour linear programming relaxation is half-integral. These instances received significant attention over ... More
An Asymptotically Optimal Channel Hopping Sequence with Maximum Rendezvous DiversityAug 01 2019In the literature, there are several well-known periodic channel hopping (CH) sequences that can achieve maximum rendezvous diversity in a cognitive radio network (CRN). For a CRN with $N$ channels, it is known that the period of such a CH sequence is ... More
Atomic Embeddability, Clustered Planarity, and ThickenabilityJul 30 2019We study the atomic embeddability testing problem, which is a common generalization of clustered planarity (c-planarity, for short) and thickenability testing, and present a polynomial time algorithm for this problem, thereby giving the first polynomial ... More
Linear Programming complementation and its application to fractional graph theoryJul 30 2019In this paper, we introduce a new kind of duality for Linear Programming (LP), that we call LP complementation. We prove that the optimal values of an LP and of its complement are in bijection (provided that either the original LP or its complement has ... More
Feasible bases for a polytope related to the Hamilton cycle problemJul 30 2019We study a certain polytope depending on a graph $G$ and a parameter $\beta\in(0,1)$ which arises from embedding the Hamiltonian cycle problem in a discounted Markov decision process. Eshragh \emph{et al.} conjectured a lower bound on the proportion of ... More
Enumeration of regular graphs by using the cluster in high efficiencyJul 29 2019In this note, we proposed a method to enumerate regular graphs on the cluster in high efficiency after partitioning. Here, we chose the GENREG, a classical regular graph generation, to adapt with supercomputers and clusters by using MPI, which can implement ... More
A Connected Version of the Graph Coloring GameJul 29 2019The graph coloring game is a two-player game in which, given a graph G and a set of k colors, the two players, Alice and Bob, take turns coloring properly an uncolored vertex of G, Alice having the first move. Alice wins the game if and only if all the ... More
Phase Transitions of Best-of-Two and Best-of-Three on Stochastic Block ModelsJul 29 2019This paper is concerned with voting processes on graphs where each vertex holds one of two different opinions. In particular, we study the \emph{Best-of-two} and the \emph{Best-of-three}. Here at each synchronous and discrete time step, each vertex updates ... More
Uniform Orderings for Generalized Coloring NumbersJul 28 2019Aug 14 2019The generalized coloring numbers scol_r(G) and wcol_r(G) of a graph G were introduced by Kierstead and Yang as a generalization of the usual coloring number, and have found important theoretical and algorithmic applications. For each distance r, these ... More
Uniform Orderings for Generalized Coloring NumbersJul 28 2019The generalized coloring numbers scol_r(G) and wcol_r(G) of a graph G were introduced by Kierstead and Yang as a generalization of the usual coloring number, and have found important theoretical and algorithmic applications. For each distance r, these ... More
Avoidable Vertices and Edges in GraphsJul 28 2019A vertex in a graph is simplicial if its neighborhood forms a clique. We consider three generalizations of the concept of simplicial vertices: avoidable vertices (also known as \textit{OCF}-vertices), simplicial paths, and their common generalization ... More
Structure of Trees with Respect to Nodal Vertex SetsJul 28 2019Let $T$ be a tree with a given adjacency eigenvalue $\lambda$. In this paper, by using the $\lambda$-minimal trees, we determine the structure of trees with a given multiplicity of the eigenvalue $\lambda$. Furthermore, we consider the relationship between ... More
Parameterized Pre-coloring Extension and List Coloring ProblemsJul 28 2019Golovach, Paulusma and Song (Inf. Comput. 2014) asked to determine the parameterized complexity of the following problems parameterized by $k$: (1) Given a graph $G$, a clique modulator $D$ (a clique modulator is a set of vertices, whose removal results ... More
Improved randomized algorithm for $k$-submodular function maximizationJul 27 2019Submodularity is one of the most important properties in combinatorial optimization, and $k$-submodularity is a generalization of submodularity. Maximization of a $k$-submodular function requires an exponential number of value oracle queries, and approximation ... More
Subtour Elimination Constraints Imply a Matrix-Tree Theorem SDP Constraint for the TSPJul 26 2019De Klerk, Pasechnik, and Sotirov give a semidefinite programming constraint for the Traveling Salesman Problem (TSP) based on the matrix-tree Theorem. This constraint says that the aggregate weight of all spanning trees in a solution to a TSP relaxation ... More
Generalized Liar's Dominating Set in GraphsJul 26 2019In this article, we study generalized liar's dominating set problem in graphs. Let $G=(V,E)$ be a simple undirected graph. The generalized liar's dominating set, called as the distance-$d$ $(m,\ell)$-liar's dominating set, is a subset $L\subseteq V$ such ... More
Integrality Gap of the Vertex Cover Linear Programming RelaxationJul 25 2019We give a characterization result for the integrality gap of the natural linear programming relaxation for the vertex cover problem. We show that integrality gap of the standard linear programming relaxation for any graph G equals $\left(2-\frac{2}{\chi^f(G)}\right)$ ... More
Polylogarithmic-Time Deterministic Network Decomposition and Distributed DerandomizationJul 25 2019We present a simple polylogarithmic-time deterministic distributed algorithm for network decomposition. This improves on a celebrated $2^{O(\sqrt{\log n})}$-time algorithm of Panconesi and Srinivasan [STOC'93] and settles one of the long-standing and ... More
GAMA: A Novel Algorithm for Non-Convex Integer ProgramsJul 25 2019Inspired by the decomposition in the hybrid quantum-classical optimization algorithm we introduced in arXiv:1902.04215, we propose here a new (fully classical) approach to solving certain non-convex integer programs using Graver bases. This method is ... More
High-Dimensional Expanders from ExpandersJul 24 2019We present an elementary way to transform an expander graph into a simplicial complex where all high order random walks have a constant spectral gap, i.e., they converge rapidly to the stationary distribution. As an upshot, we obtain new constructions, ... More
Quantum Walk over a triangular lattice subject to Pachner moveJul 24 2019Jul 27 2019We present a $2\mathrm{-dimensional}$ quantum walker on curved discrete surfaces with dynamical geometry. This walker extends the quantum walker over the fixed triangular lattice introduced in [PRA, 97(6):062111, 2018]. We write the discrete equations ... More
Quantum Walk over a triangular lattice subject to Pachner moveJul 24 2019We present a $2\mathrm{-dimensional}$ quantum walker on curved discrete surfaces with dynamical geometry. This walker extends the quantum walker over the fixed triangular lattice introduced in \cite{quantum_walk_triangular_lattice}. We write the discrete ... More
Quantum Walk over a triangular lattice subject to Pachner moveJul 24 2019Aug 12 2019We present a $2\mathrm{-dimensional}$ quantum walker on curved discrete surfaces with dynamical geometry. This walker extends the quantum walker over the fixed triangular lattice introduced in [PRA, 97(6):062111, 2018]. We write the discrete equations ... More
The stable marriage problem with ties and restricted edgesJul 24 2019In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of agents, who ... More
Medians in median graphs in linear timeJul 24 2019The median of a graph $G$ is the set of all vertices $x$ of $G$ minimizing the sum of distances from $x$ to all other vertices of $G$. It is known that computing the median of dense graphs in subcubic time refutes the APSP conjecture and computing the ... More
Reducing Path TSP to TSPJul 24 2019We present a black-box reduction from the path version of the Traveling Salesman Problem (Path TSP) to the classical tour version (TSP). More precisely, we show that given an $\alpha$-approximation algorithm for TSP, then, for any $\epsilon >0$, there ... More
Classification of linear codes using canonical augmentationJul 24 2019We propose an algorithm for classification of linear codes over different finite fields based on canonical augmentation. We apply this algorithm to obtain classification results over fields with 2, 3 and 4 elements.
Local and Union Page NumbersJul 23 2019Aug 09 2019We introduce the novel concepts of local and union book embeddings, and, as the corresponding graph parameters, the local page number ${\rm pn}_\ell(G)$ and the union page number ${\rm pn}_u(G)$. Both parameters are relaxations of the classical page number ... More
Local and Union Page NumbersJul 23 2019We introduce the novel concepts of local and union book embeddings, and, as the corresponding graph parameters, the local page number ${\rm pn}_\ell(G)$ and the union page number ${\rm pn}_u(G)$. Both parameters are relaxations of the classical page number ... More
Translating between the representations of a ranked convex geometryJul 22 2019It is well known that every closure system can be represented by an implicational base, or by the set of its meet-irreducible elements. In Horn logic, these are respectively known as the Horn expressions and the characteristic models. In this paper, we ... More
Succinct Representation for (Non)Deterministic Finite AutomataJul 22 2019Deterministic finite automata are one of the simplest and most practical models of computation studied in automata theory. Their conceptual extension is the non-deterministic finite automata which also have plenty of applications. In this article, we ... More
Robust Approach to Restricted Items Selection ProblemJul 22 2019We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version, and establish ... More
Stochastic-Greedy++: Closing the Optimality Gap in Exact Weak Submodular MaximizationJul 22 2019Many problems in discrete optimization can be formulated as the task of maximizing a monotone and weak submodular function subject to a cardinality constraint. For such problems, a simple greedy algorithm is guaranteed to find a solution with a value ... More
Semidefinite Programming Relaxations of the Traveling Salesman Problem and Their Integrality GapsJul 21 2019The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, e.g., algebraic connectivity, ... More
Logical Classification of Partially Ordered DataJul 21 2019Issues concerning intelligent data analysis occurring in machine learning are investigated. A scheme for synthesizing correct supervised classification procedures is proposed. These procedures are focused on specifying partial order relations on sets ... More
Domain Compression and its Application to Randomness-Optimal Distributed Goodness-of-FitJul 20 2019We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints. Recently, ... More
Overlapping community detection in networks based on link partitioning and partitioning around medoidsJul 20 2019In this paper, we present a new method for detecting overlapping communities in networks with a predefined number of clusters. The overlapping communities in the graph are obtained by detecting the disjoint communities in the associated line graph by ... More
Integrality of matrices, finiteness of matrix semigroups, and dynamics of linear cellular automataJul 19 2019Let $\mathbb{K}$ be a finite commutative ring, and let $\mathbb{L}$ be a commutative $\mathbb{K}$-algebra. Let $A$ and $B$ be two $n \times n$-matrices over $\mathbb{L}$ that have the same characteristic polynomial. The main result of this paper states ... More
A Practical Fixed-Parameter Algorithm for Constructing Tree-Child Networks from Multiple Binary TreesJul 19 2019We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has the minimum number of reticulations among all such networks. The algorithm uses the recently ... More
Some Polycubes Have No Edge-UnzippingJul 19 2019Jul 29 2019It is unknown whether or not every polycube has an edge-unfolding. A polycube is an object constructed by gluing cubes face-to-face. An edge-unfolding cuts edges on the surface and unfolds it to a net, a non-overlapping polygon in the plane. Here we explore ... More
Some Polycubes Have No Edge-UnzippingJul 19 2019It is unknown whether or not every polycube has an edge-unfolding. A polycube is an object constructed by gluing cubes face-to-face. An edge-unfolding cuts edges on the surface and unfolds it to a net, a non-overlapping polygon in the plane. Here we explore ... More
Finding First and Most-Beautiful Queens by Integer ProgrammingJul 18 2019The n-queens puzzle is a well-known combinatorial problem that requires to place n queens on an n x n chessboard so that no two queens can attack each other. Since the 19th century, this problem was studied by many mathematicians and computer scientists. ... More
Stack sorting with restricted stacksJul 18 2019The (classical) problem of characterizing and enumerating permutations that can be sorted using two stacks connected in series is still largely open. In the present paper we address a related problem, in which we impose restrictions both on the procedure ... More
Makespan Minimization with OR-Precedence ConstraintsJul 18 2019We consider a variant of the NP-hard problem of assigning jobs to machines to minimize the completion time of the last job. Usually, precedence constraints are given by a partial order on the set of jobs, and each job requires all its predecessors to ... More
Very fast construction of bounded-degree spanning graphs via the semi-random graph processJul 18 2019Semi-random processes involve an adaptive decision-maker, whose goal is to achieve some predetermined objective in an online randomized environment. They have algorithmic implications in various areas of computer science, as well as connections to biological ... More
On the $\text{AC}^0[\oplus]$ complexity of Andreev's ProblemJul 18 2019Andreev's Problem states the following: Given an integer $d$ and a subset of $S \subseteq \mathbb{F}_q \times \mathbb{F}_q$, is there a polynomial $y = p(x)$ of degree at most $d$ such that for every $a \in \mathbb{F}_q$, $(a,p(a)) \in S$? We show an ... More
Approximate counting CSP seen from the other sideJul 18 2019In this paper we study the complexity of counting Constraint Satisfaction Problems (CSPs) of the form #CSP($\mathcal{C}$,-), in which the goal is, given a relational structure $\mathbf{A}$ from a class $\mathcal{C}$ of structures and an arbitrary structure ... More
On the m-eternal Domination Number of Cactus GraphsJul 18 2019Given a graph $G$, guards are placed on vertices of $G$. Then vertices are subject to an infinite sequence of attacks so that each attack must be defended by a guard moving from a neighboring vertex. The m-eternal domination number is the minimum number ... More
Fast permutation-word multiplication and the simultaneous conjugacy problemJul 18 2019Given a finite sequence $a_1, a_2,\ldots, a_d$ of $d$ permutations in the symmetric group $S_n$, and a permutation word $k_1k_2\cdots k_{m}$ over the alphabet $\{1,2,\ldots, d\}$, computation of the product $a_{k_1}a_{k_2}\cdots a_{k_{m}}$ in a straightforward ... More
Linear-semiorders and their incomparability graphsJul 18 2019A linear-interval order is the intersection of a linear order and an interval order. For this class of orders, several structural results have been shown. In this paper, we study a natural subclass of linear-interval orders. We call a partial order a ... More
A study of multivalent q-starlike functions connected with circular domainJul 18 2019In the present article, our aim is to examine some useful problems including the convolution problem, sufficiency criteria, coefficient estimates and Fekete-Szego type inequalities for a new subfamily of analytic and multivalent functions associated with ... More
Solving Systems of Linear InequalitiesJul 17 2019Dantzig and Eaves claimed that fundamental duality theorems of linear programming were a trivial consequence of Fourier elimination. Another property of Fourier elimination is considered here, regarding the existence of implicit equalities rather than ... More
A Simpler Approach to Linear ProgrammingJul 17 2019Aug 21 2019Dantzig and Eaves claimed that fundamental duality theorems of linear programming were a trivial consequence of Fourier elimination. Another property of Fourier elimination is considered here, regarding the existence of implicit equalities rather than ... More