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On The Queue Number Of Planar Graphs

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Clustered planarity testing revisited

Radoslav Fulek, Jan Kyncl, Igor Malinovic

The Hanani--Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generali ...

2015

Non-Rigid Graph Registration using Active Testing Search

Pascal Fua, Raphael Sznitman, Jan Kybic, Miguel Amável Dos Santos Pinheiro

We present a new approach for matching sets of branching curvilinear structures that form graphs embedded in R2 or R3 and may be subject to deformations. Unlike earlier methods, ours does not rely on local appearance similarity nor does require a good init ...

Institute of Electrical and Electronics Engineers2015

Node-weighted network design and maximum sub-determinants

Carsten Moldenhauer

We consider the Node-weighted Steiner Forest problem on planar graphs. Demaine et al. showed that a generic primal-dual algorithm gives a 6-approximation. We present two different proofs of an approximation factor of~

3

. Then, we draw a connection to Goem ...

EPFL2014

Homometric sets in trees

Radoslav Fulek, Slobodan Mitrovic

Let G = (V, E) denote a simple graph with vertex set V and edge set E. The profile of a vertex set V' subset of V denotes the multiset of pairwise distances between the vertices of V'. Two disjoint subsets of V are homometric if their profiles are the same ...

Academic Press Ltd- Elsevier Science Ltd2014

On grids in topological graphs

János Pach

A topological graph G is a graph drawn in the plane with vertices represented by points and edges represented by continuous arcs connecting the vertices. If every edge is drawn as a straight-line segment, then G is called a geometric graph. A k-grid in a t ...

Elsevier Science Bv2014

Drawing Planar Graphs Of Bounded Degree With Few Slopes

János Pach, Balázs Keszegh, Doemoetoer Palvoelgyi

We settle a problem of Dujmovic, Eppstein, Suderman, and Wood by showing that there exists a function f with the property that every planar graph G with maximum degree d admits a drawing with noncrossing straight-line edges, using at most f(d) different sl ...

Siam Publications2013

Segmenting Planar Superpixel Adjacency Graphs w.r.t. Non-planar Superpixel Affinity Graphs

Engin Türetken

We address the problem of segmenting an image into a previously unknown number of segments from the perspective of graph partitioning. Specifically, we consider minimum multicuts of superpixel affinity graphs in which all affinities between non-adjacent su ...

2013

Efficient graph planarization in sensor networks and local routing algorithm

Florian Huc

In this paper, we propose an efficient planarization algorithm and a routing algorithm dedicated to Unit Disk Graphs whose nodes are localized using the Virtual Raw Anchor Coordinate system (VRAC). Our first algorithm computes a planar 2-spanner under ligh ...

Ieee2012

Intersection Patterns of Edges in Topological Graphs

Radoslav Fulek

This thesis is devoted to crossing patterns of edges in topological graphs. We consider the following four problems: A thrackle is a graph drawn in the plane such that every pair of edges meet exactly once: either at a common endpoint or in a proper crossi ...

EPFL2012

Drawing planar graphs of bounded degree with few slopes

János Pach, Balázs Keszegh, Doemoetoer Palvoelgyi

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2011

Node-weighted network design and maximum sub-determinants

Carsten Moldenhauer

3

. Then, we draw a connection to Goem ...

EPFL2014