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Covering Vectors by Spaces in Perturbed Graphic Matroids and Their DualsFeb 19 2019Perturbed graphic matroids are binary matroids that can be obtained from a graphic matroid by adding a noise of small rank. More precisely, r-rank perturbed graphic matroid M is a binary matroid that can be represented in the form I +P, where I is the ... More
Characterizing the Integrality Gap of the Subtour LP for the Circulant Traveling Salesman ProblemFeb 18 2019We consider the integrality gap of the subtour LP relaxation of the Traveling Salesman Problem restricted to circulant instances. De Klerk and Dobre conjectured that the value of the optimal solution to the subtour LP on these instances is equal to an ... More
Find Subtrees of Specified Weight and Cycles of Specified Length in Linear TimeFeb 18 2019We introduce a variant of DFS which finds subtrees of specified weight in linear time, by which, as observed by Mohr, cycles of specified length in planar hamiltonian graphs can be found. We show, for example, that every planar hamiltonian graph $G$ with ... More
Beating Treewidth for Average-Case Subgraph IsomorphismFeb 18 2019For any fixed graph $G$, the subgraph isomorphism problem asks whether an $n$-vertex input graph has a subgraph isomorphic to $G$. A well-known algorithm of Alon, Yuster and Zwick (1995) efficiently reduces this to the "colored" version of the problem, ... More
Braces of Perfect Matching Width 2Feb 17 2019A graph G is called matching covered if it is connected and every edge is contained in a perfect matching. Perfect matching width is a width parameter for matching covered graphs based on a branch decomposition that can be considered a generalisation ... More
Zero-Error Capacity of Duplication ChannelsFeb 17 2019This paper is motivated by the problem of error-free communication through the i.i.d. duplication channel which acts on the transmitted sequence by inserting a random number of duplicates of each symbol next to the original symbol. A construction of optimal ... More
Prophet inequality for bipartite matching: merits of being simple and non adaptiveFeb 17 2019We consider Bayesian online selection problem of a matching in bipartite graphs, i.e., online weighted matching problem with edge arrivals where online algorithm knows distributions of weights, that corresponds to the intersection of two matroids in [Kleinberg ... More
Enumerating Unique Computational Graphs via an Iterative Graph InvariantFeb 17 2019In this report, we describe a novel graph invariant for computational graphs (colored directed acylic graphs) and how we used it to generate all distinct computational graphs up to isomorphism for small graphs. The algorithm iteratively applies isomorphism-invariant ... More
Combinatorial and Algorithmic Properties of One Matrix Structure at Monotone Boolean FunctionsFeb 16 2019One matrix structure in the area of monotone Boolean functions is defined here. Some of its combinatorial, algebraic and algorithmic properties are derived. On the base of these properties, three algorithms are built. First of them generates all monotone ... More
Group testing: an information theory perspectiveFeb 15 2019The group testing problem concerns discovering a small number of defective items within a large population by performing tests on pools of items. A test is positive if the pool contains at least one defective, and negative if it contains no defectives. ... More
On long words avoiding Zimin patternsFeb 14 2019A pattern is encountered in a word if some infix of the word is the image of the pattern under some non-erasing morphism. A pattern $p$ is unavoidable if, over every finite alphabet, every sufficiently long word encounters $p$. A theorem by Zimin and ... More
Task-based Augmented Contour Trees with Fibonacci HeapsFeb 13 2019This paper presents a new algorithm for the fast, shared memory, multi-core computation of augmented contour trees on triangulations. In contrast to most existing parallel algorithms our technique computes augmented trees, enabling the full extent of ... More
List edge coloring of outer-1-planar graphsFeb 12 2019A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once. It is known that the list edge chromatic number $\chi'_l(G)$ of any outer-1-planar graph $G$ with maximum degree ... More
Graver Bases via Quantum Annealing with Application to Non-Linear Integer ProgramsFeb 12 2019We propose a novel hybrid quantum-classical approach to calculate Graver bases, which have the potential to solve a variety of hard linear and non-linear integer programs, as they form a test set (optimality certificate) with very appealing properties. ... More
DSA-aware multiple patterning for the manufacturing of vias: Connections to graph coloring problems, IP formulations, and numerical experimentsFeb 11 2019In this paper, we investigate the manufacturing of vias in integrated circuits with a new technology combining lithography and Directed Self Assembly (DSA). Optimizing the production time and costs in this new process entails minimizing the number of ... More
On the number of pancake stacks requiring 4 flips to be sortedFeb 11 2019Using an existing classification results for the 7- and 8-cycles in the pancake graph, we determine the number of permutations that require 4 pancake flips (prefix reversals) to be sorted. A similar characterization of the 8-cycles in the burnt pancake ... More
All those EPPA classes (Strengthenings of the Herwig-Lascar theorem)Feb 11 2019In this paper we prove a general theorem showing the extension property for partial automorphisms (EPPA, also called the Hrushovski property) for classes of structures containing relations and unary functions, optionally equipped with a permutation group ... More
Flexibility of planar graphs of girth at least sixFeb 11 2019Let G be a planar graph with a list assignment L. Suppose a preferred color is given for some of the vertices. We prove that if G has girth at least six and all lists have size at least three, then there exists an L-coloring respecting at least a constant ... More
Set Cover in Sub-linear TimeFeb 10 2019We study the classic set cover problem from the perspective of sub-linear algorithms. Given access to a collection of $m$ sets over $n$ elements in the query model, we show that sub-linear algorithms derived from existing techniques have almost tight ... More
Two-tier blockchain timestamped notarization with incremental securityFeb 08 2019Digital notarization is one of the most promising services offered by modern blockchain-based solutions. We present a digital notary design with incremental security and cost reduced with respect to current solutions. A client of the service receives ... More
On the Broadcast Independence Number of Locally Uniform 2-LobstersFeb 08 2019Let $G$ be a simple undirected graph.A broadcast on $G$ isa function $f : V(G) \to \mathbf{N}$ such that $f(v)\le e_G(v)$ holds for every vertex $v$ of $G$, where $e_G(v)$ denotes the eccentricity of $v$ in $G$, that is, the maximum distance from $v$ ... More
Flexibility of triangle-free planar graphsFeb 08 2019Let G be a planar graph with a list assignment L. Suppose a preferred color is given for some of the vertices. We prove that if G is triangle-free and all lists have size at least four, then there exists an L-coloring respecting at least a constant fraction ... More
Going Far From DegeneracyFeb 07 2019Feb 14 2019An undirected graph G is d-degenerate if every subgraph of G has a vertex of degree at most d. By the classical theorem of Erd\H{o}s and Gallai from 1959, every graph of degeneracy d>1 contains a cycle of length at least d+1. The proof of Erd\H{o}s and ... More
Going Far From DegeneracyFeb 07 2019An undirected graph G is d-degenerate if every subgraph of G has a vertex of degree at most d. By the classical theorem of Erd\H{o}s and Gallai from 1959, every graph of degeneracy d>1 contains a cycle of length at least d+1. The proof of Erd\H{o}s and ... More
On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matricesFeb 06 2019The problem of finding a $k \times k$ submatrix of maximum volume of a matrix $A$ is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of $A$. We show that such a ... More
Reconfiguring 10-colourings of planar graphsFeb 06 2019Let $k \geq 1$ be an integer. The reconfiguration graph $R_k(G)$ of the $k$-colourings of a graph~$G$ has as vertex set the set of all possible $k$-colourings of $G$ and two colourings are adjacent if they differ on exactly one vertex. A conjecture of ... More
Information-theoretic and algorithmic thresholds for group testingFeb 06 2019In the group testing problem we aim to identify a small number of infected individuals within a large population. We avail ourselves to a procedure that can test a group of multiple individuals, with the test result coming out positive iff at least one ... More
Exact Markov Chain-based Runtime Analysis of a Discrete Particle Swarm Optimization Algorithm on Sorting and OneMaxFeb 05 2019We present a comprehensive analysis of a discrete particle swarm optimization (PSO) algorithm that can be adapted to work on a large class of discrete optimization problems. For this purpose, we model the algorithm's behavior by Markov chains with different ... More
An Optimal Algorithm for Online Freeze-tagFeb 05 2019In the freeze-tag problem, one active robot must wake up many frozen robots. The robots are considered as points in a metric space, where active robots move at a constant rate and activate other robots by visiting them. In the (time-dependent) online ... More
Cyclewidth and the Grid Theorem for Perfect Matching Width of Bipartite GraphsFeb 04 2019Feb 05 2019A connected graph G is called matching covered if every edge of G is contained in a perfect matching. Perfect matching width is a width parameter for matching covered graphs based on a branch decomposition. It was introduced by Norine and intended as ... More
Cyclewidth and the Grid Theorem for Perfect Matching Width of Bipartite GraphsFeb 04 2019Feb 14 2019A connected graph G is called matching covered if every edge of G is contained in a perfect matching. Perfect matching width is a width parameter for matching covered graphs based on a branch decomposition. It was introduced by Norine and intended as ... More
Stabilization Time in Weighted Minority ProcessesFeb 04 2019A minority process in a weighted graph is a dynamically changing coloring. Each node repeatedly changes its color in order to minimize the sum of weighted conflicts with its neighbors. We study the number of steps until such a process stabilizes. Our ... More
A Faster FPTAS for Knapsack Problem With Cardinality ConstraintFeb 03 2019Feb 13 2019We study the $K$-item knapsack problem (\ie, $1.5$-dimensional KP), which is a generalization of the famous 0-1 knapsack problem (\ie, $1$-dimensional KP) in which an upper bound $K$ is imposed on the number of items selected. This problem is of fundamental ... More
Knapsack Problem With Cardinality Constraint: A Faster FPTAS Through the Lens of Numerical Analysis and ApplicationsFeb 03 2019We study the $K$-item knapsack problem (\ie, $1.5$-dimensional knapsack problem), which is a generalization of the famous 0-1 knapsack problem (\ie, $1$-dimensional knapsack problem) in which an upper bound $K$ is imposed on the number of items selected. ... More
Eternal domination on prisms of graphsFeb 02 2019An eternal dominating set of a graph $G$ is a set of vertices (or "guards") which dominates $G$ and which can defend any infinite series of vertex attacks, where an attack is defended by moving one guard along an edge from its current position to the ... More
The Applications of Graph Theory to InvestingFeb 02 2019How can graph theory be applied to investing in the stock market? The answer may help investors realize the true risks of their investments, help prevent recessions like that of 2008, and increase financial literacy amongst students. Using several original ... More
Some Enumeration Problems in the Duplication-Loss Model of Genome RearrangementFeb 01 2019Tandem-duplication-random-loss (TDRL) is an important genome rearrangement operation studied in evolutionary biology. This paper investigates some of the formal properties of TDRL operations on the symmetric group (the space of permutations over an $ ... More
On two-fold packings of radius-1 balls in Hamming graphsJan 31 2019A $\lambda$-fold $r$-packing in a Hamming metric space is a code $C$ such that the radius-$r$ balls centered in $C$ cover each vertex of the space by not more than $\lambda$-times. The well-known $r$-error-correcting codes correspond to the case $\lambda=1$. ... More
On $(2n/3-1)$-resilient $(n,2)$-functionsJan 31 2019A $\{00,01,10,11\}$-valued function on the vertices of the $n$-cube is called a $t$-resilient $(n,2)$-function if it has the same number of $00$s, $01$s, $10$s and $11$s among the vertices of every subcube of dimension $t$. The Friedman and Fon-Der-Flaass ... More
On dual codes in the Doob schemesJan 31 2019The Doob scheme $D(m,n'+n'')$ is a metric association scheme defined on $E_4^m \times F_4^{n'}\times Z_4^{n''}$, where $E_4=GR(4^2)$ or, alternatively, on $Z_4^{2m} \times Z_2^{2n'} \times Z_4^{n''}$. We prove the MacWilliams identities connecting the ... More
Algorithmic counting of nonequivalent compact Huffman codesJan 31 2019It is known that the following five counting problems lead to the same integer sequence~$f_t(n)$: the number of nonequivalent compact Huffman codes of length~$n$ over an alphabet of $t$ letters, the number of `nonequivalent' canonical rooted $t$-ary trees ... More
The smallest nontrivial snarks of oddness 4Jan 30 2019The oddness of a cubic graph is the smallest number of odd circuits in a 2-factor of the graph. This invariant is widely considered to be one of the most important measures of uncolourability of cubic graphs and as such has been repeatedly reoccurring ... More
Short cycle covers of cubic graphs and intersecting 5-circuitsJan 30 2019A cycle cover of a graph is a collection of cycles such that each edge of the graph is contained in at least one of the cycles. The length of a cycle cover is the sum of all cycle lengths in the cover. We prove that every bridgeless cubic graph with $m$ ... More
A Pseudo-Deterministic RNC Algorithm for General Graph Perfect MatchingJan 29 2019Jan 31 2019We give an NC reduction from search to decision for the problem of finding a minimum weight perfect matching, provided edge weights are polynomially bounded. As a consequence, for settling the long-standing open problem of obtaining an NC perfect matching ... More
On the distance $α$-spectral radius of a connected graphJan 29 2019For a connected graph $G$ and $\alpha\in [0,1)$, the distance $\alpha$-spectral radius of $G$ is the spectral radius of the matrix $D_{\alpha}(G)$ defined as $D_{\alpha}(G)=\alpha T(G)+(1-\alpha)D(G)$, where $T(G)$ is a diagonal matrix of vertex transmissions ... More
Heterogeneous Network MotifsJan 28 2019Feb 04 2019Many real-world applications give rise to large heterogeneous networks where nodes and edges can be of any arbitrary type (e.g., user, web page, location). Special cases of such heterogeneous graphs include homogeneous graphs, bipartite, k-partite, signed, ... More
Triangle-degrees in graphs and tetrahedron coverings in 3-graphsJan 28 2019We investigate a covering problem in $3$-uniform hypergraphs ($3$-graphs): given a $3$-graph $F$, what is $c_1(n,F)$, the least integer $d$ such that if $G$ is an $n$-vertex $3$-graph with minimum vertex degree $\delta_1(G)>d$ then every vertex of $G$ ... More
Large Minors in ExpandersJan 27 2019Jan 29 2019In this paper we study expander graphs and their minors. Specifically, we attempt to answer the following question: what is the largest function $f(n,\alpha,d)$, such that every $n$-vertex $\alpha$-expander with maximum vertex degree at most $d$ contains ... More
Recycling Solutions for Vertex Coloring HeuristicsJan 27 2019The vertex coloring problem is a well-known NP-hard problem and has many applications 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 ... More
Beyond the Erdős Matching ConjectureJan 26 2019Feb 05 2019A family $\mathcal F\subset {[n]\choose k}$ is $U(s,q)$ of for any $F_1,\ldots, F_s\in \mathcal F$ we have $|F_1\cup\ldots\cup F_s|\le q$. This notion generalizes the property of a family to be $t$-intersecting and to have matching number smaller than ... More
No-three-in-line problem on a torus: periodicityJan 25 2019Let $\tau_{m,n}$ denote the maximal number of points on the discrete torus (discrete toric grid) of sizes $m \times n$ with no three collinear points. The value $\tau_{m,n}$ is known for the case where $\gcd(m,n)$ is prime. It is also known that $\tau_{m,n} ... More
A Sublinear Bound on the Cop Throttling Number of a GraphJan 25 2019We provide a sublinear bound on the cop throttling number of a connected graph. Related to the graph searching game Cops and Robbers, the cop throttling number, written $\mathrm{th}_c(G)$, is given by $\mathrm{th}_c(G)=\min_k\{k+\mathrm{capt}_k(G)\}$, ... More
A structure theorem for almost low-degree functions on the sliceJan 25 2019The Fourier-Walsh expansion of a Boolean function $f \colon \{0,1\}^n \rightarrow \{0,1\}$ is its unique representation as a multilinear polynomial. The Kindler-Safra theorem (2002) asserts that if in the expansion of $f$, the total weight on coefficients ... More
Infinite All-Layers Simple FoldabilityJan 24 2019We study the problem of deciding whether a crease pattern can be folded by simple folds (folding along one line at a time) under the infinite all-layers model introduced by [Akitaya et al., 2017], in which each simple fold is defined by an infinite line ... More
Towards Tight(er) Bounds for the Excluded Grid TheoremJan 23 2019We study the Excluded Grid Theorem, a fundamental structural result in graph theory, that was proved by Robertson and Seymour in their seminal work on graph minors. The theorem states that there is a function $f: \mathbb{Z}^+ \to \mathbb{Z}^+$, such that ... More
Embedding quadratization gadgets on Chimera and Pegasus graphsJan 23 2019We group all known quadratizations of cubic and quartic terms in binary optimization problems into six and seven unique graphs respectively. We then perform a minor embedding of these graphs onto the well-known Chimera graph, and the brand new Pegasus ... More
Pegasus: The second connectivity graph for large-scale quantum annealing hardwareJan 22 2019Pegasus is a graph which offers substantially increased connectivity between the qubits of quantum annealing hardware compared to the graph Chimera. It is the first fundamental change in the connectivity graph of quantum annealers built by D-Wave since ... More
Partial Order on the set of Boolean Regulatory FunctionsJan 22 2019Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a given model a ... More
Palindromic Subsequences in Finite WordsJan 22 2019In 1999 Lyngs{\o} and Pedersen proposed a conjecture stating that every binary circular word of length $n$ with equal number of zeros and ones has an antipalindromic linear subsequence of length at least $\frac{2}{3}n$. No progress over a trivial $\frac{1}{2}n$ ... More
Solve For Shortest Paths Problem Within Logarithm RuntimeJan 22 2019The Shortest Paths Problem (SPP) is no longer unresolved. Just for a large scalar of instance on this problem, even we cannot know if an algorithm achieves the computing. Those cutting-edge methods are still in the low performance. If we go to a strategy ... More
On random multi-dimensional assignment problemsJan 22 2019We study random multidimensional assignment problems where the costs decompose into the sum of independent random variables. In particular, in three dimensions, we assume that the costs $W_{i,j,k}$ satisfy $W_{i,j,k}=a_{i,j}+b_{i,k}+c_{j,k}$ where the ... More
Constrained path-finding and structure from acyclicityJan 21 2019This note presents several results in graph theory inspired by the author's work in the proof theory of linear logic; these results are purely combinatorial and do not involve logic. We show that trails avoiding forbidden transitions and rainbow paths ... More
Computing Optimal Tangles FasterJan 19 2019We study the following combinatorial problem. Given a set of $n$ y-monotone wires, a tangle determines the order of the wires on a number of horizontal layers such that the orders of the wires on any two consecutive layers differ only in swaps of neighboring ... More
Towards a General Direct Product Testing TheoremJan 18 2019The Direct Product encoding of a string $a\in \{0,1\}^n$ on an underlying domain $V\subseteq \binom{n}{k}$, is a function DP$_V(a)$ which gets as input a set $S\in V$ and outputs $a$ restricted to $S$. In the Direct Product Testing Problem, we are given ... More
Extremality and Sharp Bounds for the $k$-edge-connectivity of GraphsJan 18 2019Boesch and Chen (SIAM J. Appl. Math., 1978) introduced the cut-version of the generalized edge-connectivity, named $k$-edge-connectivity. For any integer $k$ with $2\leq k\leq n$, the {\em $k$-edge-connectivity} of a graph $G$, denoted by $\lambda_k(G)$, ... More
Hamiltonian chromatic number of block graphsJan 17 2019Let $G$ be a simple connected graph of order $n$. A hamiltonian coloring $c$ of a graph $G$ is an assignment of colors (non-negative integers) to the vertices of $G$ such that $D(u, v)$ + $|c(u) - c(v)|$ $\geq$ $n - 1$ for every two distinct vertices ... More
Queue Layouts of Graphs with Bounded Degree and Bounded GenusJan 17 2019We prove that graphs with bounded degree and bounded Euler genus have bounded queue-number. As a byproduct we prove that if planar graphs have bounded queue-number (which is an open problem), then graphs of Euler genus $g$ have queue-number $O(g)$.
On Extremal Graphs of Weighted Szeged IndexJan 15 2019An extension of the well-known Szeged index was introduced recently, named as weighted Szeged index ($\textrm{sz}(G)$). This paper is devoted to characterizing the extremal trees and graphs of this new topological invariant. In particular, we proved that ... More
A constant parameterized approximation for hard-capacitated k-meansJan 15 2019Hard-capacitated k-means (HCKM) is one of the remaining fundamental problems for which if there exist polynomial time constant factor approximation is not clear. But what we know is that it is at least APX-hard. Most of the existing as well as the state-of-the-art ... More
Extending partial isometries of antipodal graphsJan 14 2019We prove EPPA (extension property for partial automorphisms) for all antipodal classes from Cherlin's list of metrically homogeneous graphs, thereby answering a question of Aranda et al. This paper should be seen as the first application of a new general ... More
Quadratization in discrete optimization and quantum mechanicsJan 14 2019A book about turning high-degree optimization problems into quadratic optimization problems that maintain the same global minimum (ground state). This book explores quadratizations for pseudo-Boolean optimization, perturbative gadgets used in QMA completeness ... More
A lower bound on the tree-width of graphs with irrelevant verticesJan 14 2019For their famous algorithm for the disjoint paths problem, Robertson and Seymour proved that there is a function $f$ such that if the tree-width of a graph $G$ with $k$ pairs of terminals is at least $f(k)$, then $G$ contains a solution-irrelevant vertex ... More
The range of non-linear natural polynomials cannot be context-freeJan 12 2019Suppose that some polynomial $f$ with rational coefficients takes only natural values at natural numbers, i.e., $L=\{f(n)\mid n\in \mathbb N\}\subset\mathbb N$. We show that the base-$k$ representation of $L$ is a context-free language if and only if ... More
Simple juntas for shifted familiesJan 12 2019Jan 20 2019We say that a family $\mathcal F$ of $k$-element sets is a $j$-junta if there is a set $J$ of size $j$ such that, for any $F$, its presence in $\mathcal F$ depends on its intersection with $J$ only. Approximating arbitrary families by $j$-juntas with ... More
Destroying Bicolored $P_3$s by Deleting Few EdgesJan 11 2019We introduce and study the Bicolored $P_3$ Deletion problem defined as follows. The input is a graph $G=(V,E)$ where the edge set $E$ is partitioned into a set $E_b$ of blue edges and a set $E_r$ of red edges. The question is whether we can delete at ... More
Graph embeddings into Hamming spacesJan 10 2019Graph embeddings deal with injective maps from a given simple, undirected graph $G=(V,E)$ into a metric space, such as $\mathbb{R}^n$ with the Euclidean metric. This concept is widely studied in computer science, see \cite{ge1}, but also offers attractive ... More
Proof of a conjecture on the algebraic connectivity of a graph and its complementJan 07 2019For a graph $G$, let $\lambda_2(G)$ denote its second smallest Laplacian eigenvalue. It was conjectured that $\lambda_2(G) + \lambda_2(\overline{G}) \geq 1$, where $\bar{G}$ is the complement of $G$. Here, we prove this conjecture in the general case. ... More
On the Parameterized Complexity of $k$-Edge ColouringJan 07 2019Jan 08 2019For every fixed integer $k \geq 1$, we prove that $k$-Edge Colouring is fixed-parameter-tractable when parameterized by the number of vertices of maximum degree.
Baker game and polynomial-time approximation schemesJan 07 2019Baker devised a technique to obtain approximation schemes for many optimization problems restricted to planar graphs; her technique was later extended to more general graph classes. In particular, using the Baker's technique and the minor structure theorem, ... More
Search Space Reduction of Asynchrony Immune Cellular Automata by Center PermutivityJan 06 2019We continue the study of asynchrony immunity in cellular automata (CA), which can be considered as a weaker version of correlation immunity in the context of vectorial Boolean functions. The property could have applications as a countermeasure for side-channel ... More
On the Implementation and Assessment of several Divide & Conquer Matheuristic Strategies for the solution of the Knapsack ProblemJan 04 2019We introduce and asses a Divide \& Conquer heuristic method, aimed to solve large instances of the Knapsack Problem. The method subdivides a large problem in two smaller ones (or recursive iterations of the same principle), to lower down the global computational ... More
A modified greedy algorithm to improve bounds for the vertex cover numberJan 03 2019In any attempt at designing an efficient algorithm for the minimum vertex cover problem, obtaining good upper and lower bounds for the vertex cover number could be crucial. In this article we present a modified greedy algorithm of worst-case time complexity ... More
Clique-Width for Hereditary Graph ClassesJan 02 2019Jan 07 2019Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class ${\cal G}$ is bounded by a constant, a wide range of problems that are NP-complete in general can be shown ... More
Inference under Information Constraints I: Lower Bounds from Chi-Square ContractionDec 30 2018Feb 09 2019Multiple players are each given one independent sample, about which they can only provide limited information to a central referee. Each player is allowed to describe its observed sample to the referee using a channel from a family of channels $\mathcal{W}$, ... More
Convex Polygons in Cartesian ProductsDec 29 2018We study several problems concerning convex polygons whose vertices lie in a Cartesian product (for short, grid) of two sets of n real numbers. First, we prove that every such grid contains a convex polygon with $\Omega$(log n) vertices and that this ... More
EPPA for two-graphs and antipodal metric spacesDec 28 2018We prove that the class of two-graphs has the extension property for partial automorphisms (EPPA, or Hrushovski property), thereby answering a question of Macpherson. In other words, we show that the class of graphs has the extension property for switching ... More
Occupancy fraction, fractional colouring, and triangle fractionDec 28 2018Given $\varepsilon>0$, there exists $f_0$ such that, if $f_0 \le f \le \Delta^2+1$, then for any graph $G$ on $n$ vertices of maximum degree $\Delta$ in which the neighbourhood of every vertex in $G$ spans at most $\Delta^2/f$ edges, (i) an independent ... More
Isolation of $k$-cliquesDec 28 2018For any positive integer $k$ and any $n$-vertex graph $G$, let $\iota(G,k)$ denote the size of a smallest set $D$ of vertices of $G$ such that the graph obtained from $G$ by deleting the closed neighbourhood of $D$ contains no $k$-clique. Thus, $\iota(G,1)$ ... More
A Precedent Approach to Assigning Access RightsDec 28 2018To design a discretionary access control policy, a technique is proposed that uses the principle of analogies and is based on both the properties of objects and the properties of subjects. As attributes characterizing these properties, the values of the ... More
On $(1+\varepsilon)$-approximate problem kernels for the Rural Postman ProblemDec 25 2018Given a graph $G=(V,E)$ with edge weights $\omega\colon E\to\mathbb N\cup\{0\}$ and a subset $R\subseteq E$ of edges, the Rural Postman Problem (RPP) is to find a closed walk $W^*$ of minimum weight $\omega(W^*)$ containing all edges of $R$. We prove ... More
Propagation time for probabilistic zero forcingDec 24 2018Zero forcing is a coloring game played on a graph that was introduced more than ten years ago in several different applications. The goal is to color all the vertices blue by repeated use of a (deterministic) color change rule. Probabilistic zero forcing ... More
Cops, robbers, and burning bridgesDec 24 2018We consider a variant of Cops and Robbers wherein each edge traversed by the robber is deleted from the graph. The focus is on determining the minimum number of cops needed to capture a robber on a graph $G$, called the {\em bridge-burning cop number} ... More
Lower bounds on the chromatic number of random graphsDec 23 2018We prove that a formula predicted on the basis of non-rigorous physics arguments [Zdeborova and Krzakala: Phys. Rev. E (2007)] provides a lower bound on the chromatic number of sparse random graphs. The proof is based on the interpolation method from ... More
Packing functions and graphs with perfect closed neighbourhood matricesDec 22 2018In this work we consider a straightforward linear programming formulation of the recently introduced $\{k\}$-packing function problem in graphs, for each fixed value of the positive integer number $k$. We analyse a special relation between the case $ ... More
Using First Hitting Times to Find Sets that Maximize the Convergence Rate to ConsensusDec 20 2018In a model of communication in a social network described by a simple consensus model, we pose the problem of finding a subset of nodes with given cardinality and fixed consensus values that enable the fastest convergence rate to equilibrium of the values ... More
Vertex-Facet Assignments For PolytopesDec 20 2018For polytopes in $\mathbb{R}^d$ with at least as many facets as vertices, we prove that vertices can be mapped injectively to non-incident facets when $1\leq d\leq 5$ and give counterexamples for $d\geq 7$.
Iterated Belief Revision Under Resource Constraints: Logic as GeometryDec 20 2018We propose a variant of iterated belief revision designed for settings with limited computational resources, such as mobile autonomous robots. The proposed memory architecture---called the {\em universal memory architecture} (UMA)---maintains an epistemic ... More
On zero-free regions for the anti-ferromagnetic Potts model on bounded-degree graphsDec 18 2018For a graph $G=(V,E)$, $k\in \mathbb{N}$, and a complex number $w$ the partition function of the univariate Potts model is defined as \[ {\bf Z}(G;k,w):=\sum_{\phi:V\to [k]}\prod_{\substack{uv\in E \\ \phi(u)=\phi(v)}}w. \] In this paper we give zero-free ... More
Computing the $k$-binomial complexity of the Thue--Morse wordDec 18 2018Two words are $k$-binomially equivalent whenever they share the same subwords, i.e., subsequences, of length at most $k$ with the same multiplicities. This is a refinement of both abelian equivalence and the Simon congruence. The $k$-binomial complexity ... More
Model-Checking on Ordered StructuresDec 18 2018We study the model-checking problem for first- and monadic second-order logic on finite relational structures. The problem of verifying whether a formula of these logics is true on a given structure is considered intractable in general, but it does become ... More