Related papers: A meet-in-the-middle algorithm for finding extrema…
Max cones are max-algebraic analogs of convex cones. In the present paper we develop a theory of generating sets and extremals of max cones in ${{\mathbb R}}_+^n$. This theory is based on the observation that extremals are minimal elements…
Confidence intervals are a standard technique for analyzing data. When applied to time series, confidence intervals are computed for each time point separately. Alternatively, we can compute confidence bands, where we are required to find…
We study Abelian sandpiles on graphs of the form $G \times I$, where $G$ is an arbitrary finite connected graph, and $I \subset \Z$ is a finite interval. We show that for any fixed $G$ with at least two vertices, the stationary measures…
An upper dominating set is a minimal dominating set in a graph. In the \textsc{Upper Dominating Set} problem, the goal is to find an upper dominating set of maximum size. We study the complexity of parameterized algorithms for \textsc{Upper…
We present an exact algorithm that decides, for every fixed $r \geq 2$ in time $O(m) + 2^{O(k^2)}$ whether a given multiset of $m$ clauses of size $r$ admits a truth assignment that satisfies at least $((2^r-1)m+k)/2^r$ clauses. Thus…
A spherical two-distance set is a finite collection of unit vectors in $\reals^n$ such that the set of distances between any two distinct vectors has cardinality two. We use the semidefinite programming method to compute improved estimates…
A mixed dominating set is a collection of vertices and edges that dominates all vertices and edges of a graph. We study the complexity of exact and parameterized algorithms for \textsc{Mixed Dominating Set}, resolving some open questions.…
In this paper we deal with a Tur\'an-type problem: given a positive integer n and a forbidden graph H, how many edges can there be in a graph on n vertices without a subgraph H? How does a graph look like if it has this extremal edge…
In the (binary) Distinct Vectors problem we are given a binary matrix A with pairwise different rows and want to select at most k columns such that, restricting the matrix to these columns, all rows are still pairwise different. A result by…
We study the problem of computing the \textsc{Maxima} of a set of $n$ $d$-dimensional points. For dimensions 2 and 3, there are algorithms to solve the problem with order-oblivious instance-optimal running time. However, in higher…
An extremity is a vertex such that the removal of its closed neighbourhood does not increase the number of connected components. Let $Ext_{\alpha}$ be the class of all connected graphs whose quotient graph obtained from modular…
}We study (vertex-disjoint) $P_2$-packings in graphs under a parameterized perspective. Starting from a maximal $P_2$-packing $\p$ of size $j$ we use extremal arguments for determining how many vertices of $\p$ appear in some $P_2$-packing…
We study the problem of finding a \textit{maximal} transitive relation contained in a given binary relation. Given a binary relation of size $m$ defined on a set of size $n$, we present a polynomial time algorithm that finds a maximal…
In this paper, a virus optimization algorithm, which is one of the metaheuristic optimization technique, is employed for the first time to the problem of finding extremal binary self-dual codes. We present a number of generator matrices of…
New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose vertices all lie within an $n$-point subset of the plane is…
We consider the average distance between four bases in dimension six. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We…
The problem of optimal antipodal codes can be framed as finding low rank Gram matrices $G$ with $G_{ii} = 1$ and $|G_{ij}| \leq \epsilon$ for $1 \leq i \neq j \leq n$. In 2018, Bukh and Cox introduced a new bounding technique by removing…
In connection with optimal state determination for two qubits, the question was raised about the maximum number of pairwise complementary reductions. The main result of the paper tells that the maximum number is 4, that is, if A1, A2,... Ak…
We show that the amoeba of a complex algebraic variety defined as the solutions to a generic system of $n$ polynomials in $n$ variables has a finite basis. In other words, it is the intersection of finitely many hypersurface amoebas.…
In this paper, we propose a column by column encoding scheme suitable for two-dimensional (2D) constraint codes and derive a lower bound of its maximum achievable rate. It is shown that the maximum achievable rate is equal to the largest…