Related papers: The Peculiarities of Extending Queue Layouts
Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…
The Seat Arrangement Problem is a problem of finding a desirable seat arrangement for given preferences of agents and a seat graph that represents a configuration of seats. In this paper, we consider decision problems of determining if an…
An $h$-queue layout of a graph $G$ consists of a linear order of its vertices and a partition of its edges into $h$ queues, such that no two independent edges of the same queue nest. The minimum $h$ such that $G$ admits an $h$-queue layout…
Given a collection $L$ of line segments, we consider its arrangement and study the problem of covering all cells with line segments of $L$. That is, we want to find a minimum-size set $L'$ of line segments such that every cell in the…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
Priority queues are one of the most fundamental and widely used data structures in computer science. Their primary objective is to efficiently support the insertion of new elements with assigned priorities and the extraction of the highest…
In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multivariate polynomials, and only a small…
We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the…
We present a prototype online system to automate the procedure of computing different types of linear layouts of graphs under different user-specific constraints. Currently, four different types of linear layouts are supported: stack,…
A mixed s-stack q-queue layout of a graph consists of a linear order of its vertices and of a partition of its edges into s stacks and q queues, such that no two edges in the same stack cross and no two edges in the same queue nest. In…
The recently introduced problem of extending partial interval representations asks, for an interval graph with some intervals pre-drawn by the input, whether the partial representation can be extended to a representation of the entire…
Given an underlying undirected simple graph, we consider the set of all acyclic orientations of its edges. Each of these orientations induces a partial order on the vertices of our graph and, therefore, we can count the number of linear…
Paging is a prototypical problem in the area of online algorithms. It has also played a central role in the development of learning-augmented algorithms -- a recent line of research that aims to ameliorate the shortcomings of classical…
We study the problem of connecting the parts of a multipartite graph using a minimum number of edges under a matching constraint. We introduce interconnection trees, defined as matchings whose projections onto the quotient graph form a…
The queue-number of a poset is the queue-number of its cover graph viewed as a directed acyclic graph, i.e., when the vertex order must be a linear extension of the poset. Heath and Pemmaraju conjectured that every poset of width $w$ has…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…
Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet,…
In this paper we give an overview of the graph invariants queue number and stack number (the latter also called the page number or book thickness). Due to their similarity, it has been studied for a long time, whether one of them is bounded…
We consider the following online optimization problem. We are given a graph $G$ and each vertex of the graph is assigned to one of $\ell$ servers, where servers have capacity $k$ and we assume that the graph has $\ell \cdot k$ vertices.…