Related papers: Planar Maps in 4 bits/edge

We present a general bijective approach to planar hypermaps with two main results. First we obtain unified bijections for all classes of maps or hypermaps defined by face-degree constraints and girth constraints. To any such class we…

Multidimensional optical signals are commonly recorded by varying the delays between time ordered pulses. These control the evolution of the density matrix and are described by ladder diagrams. We propose a new non-time-ordered protocol…

We give a parallel $O(\log(n))$-time algorithm on a CRCW PRAM to assign vertical and horizontal segments to the vertices of any planar bipartite graph $G$ in the following manner: i) Two segments cannot share an interior point ii) Two…

We show, without using the Four Color Theorem, that for each planar triangulation, the number of its proper vertex colorings by 4 colors is a determinant and thus can be calculated in a polynomial time. In particular, we can efficiently…

The problem of map enumeration concerns counting connected spatial graphs, with a specified number $j$ of vertices, that can be embedded in a compact surface of genus $g$ in such a way that its complement yields a cellular decomposition of…

For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…

Canonical orderings serve as the basis for many incremental planar drawing algorithms. All these techniques, however, have in common that they are limited to undirected graphs. While $st$-orderings do extend to directed graphs, especially…

In a rectilinear dual of a planar graph vertices are represented by simple rectilinear polygons and edges are represented by side-contact between the corresponding polygons. A rectilinear dual is called a cartogram if the area of each…

We design a network coding scheme with minimum reception overhead and linear encoding/decoding complexity.

Median graphs are connected graphs in which for all three vertices there is a unique vertex that belongs to shortest paths between each pair of these three vertices. In this paper we provide several novel characterizations of planar median…

In this article we consider the action of affine group and time rescaling on planar quadratic differential systems. We construct a system of representatives of the orbits of systems with four invariant lines, including the line at infinity…

In this paper, we consider the problem of representing graphs by polygons whose sides touch. We show that at least six sides per polygon are necessary by constructing a class of planar graphs that cannot be represented by pentagons. We also…

We study path-based graph queries that, in addition to navigation through edges, also perform navigation through time. This allows asking questions about the dynamics of networks, like traffic movement, cause-effect relationships, or the…

A distance labeling scheme is an assignments of labels, that is binary strings, to all nodes of a graph, so that the distance between any two nodes can be computed from their labels and the labels are as short as possible. A major open…

Polar codes are widely used in modern communication systems due to their capacity-achieving properties. This paper investigates the importance of coded bits in the decoding process of polar codes and aims to determine which bits contribute…

In previous work, we demonstrated how decoding of a non-binary linear code could be formulated as a linear-programming problem. In this paper, we study different polytopes for use with linear-programming decoding, and show that for many…

We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…

Compact representations of objects is a common concept in computer science. Automated planning can be viewed as a case of this concept: a planning instance is a compact implicit representation of a graph and the problem is to find a path (a…

Given a finite or infinite planar graph all of whose faces have degree 4, we study embeddings in the plane in which all edges have length 1, that is, in which every face is a rhombus. We give a necessary and sufficient condition for the…

We prove a general multi-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers…