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Random walks and forbidden minors III: poly(d epsilon(-1))-time partition oracles for minor-free graph classes

Related publications (211)

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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

Decomposition and tractability in qualitative spatial and temporal reasoning

Jingshi Li

Constraint networks in qualitative spatial and temporal reasoning (QSTR) typically feature variables defined on infinite domains. Mainstream algorithms for deciding network consistency are based on searching for network refinements whose consistency is kno ...

Elsevier2013

Intelligent Clustering for Graph Visualization

Lionel Jérémie Martin

More and more areas use graphs for the representation of their data because it gives a connection-oriented perspective. Unfortunately, datasets are constantly growing in size, while devices have increasingly smaller screens (tablets, smartphones, etc). In ...

2013

Tangles and Degenerate Tangles

Andres Jacinto Ruiz Vargas

We study some variants of Conway’s thrackle conjecture. A tangle is a graph drawn in the plane such that its edges are represented by continuous arcs, and any two edges share precisely one point, which is either a common endpoint or an interior point at wh ...

Springer Berlin Heidelberg2013

Coloring Triangle-Free Rectangular Frame Intersection Graphs with O(loglogn) Colors

Bartosz Maria Walczak

Recently, Pawlik et al. have shown that triangle-free intersection graphs of line segments in the plane can have arbitrarily large chromatic number. Specifically, they construct triangle-free segment intersection graphs with chromatic number Θ(log log n). ...

2013

New Bounds on the Maximum Number of Edges in k-Quasi-Planar Graphs

Bartosz Maria Walczak

A topological graph is k-quasi-planar if it does not contain k pairwise crossing edges. An old conjecture states that for every fixed k, the maximum number of edges in a k-quasi-planar graph on n vertices is O(n). Fox and Pach showed that every k-quasi-pla ...

Springer International Publishing2013

On The Queue Number Of Planar Graphs

János Pach, Fabrizio Frati

We prove that planar graphs have O(log(2) n) queue number, thus improving upon the previous O(root n) upper bound. Consequently, planar graphs admit three-dimensional straight-line crossing-free grid drawings in O(n log(8) n) volume, thus improving upon th ...

Siam Publications2013

Optimizing Mix-zone Coverage in Pervasive Wireless Networks

Jean-Pierre Hubaux, Murtuza Jadliwala, Igor Bilogrevic

Location privacy is a major concern in pervasive networks where static device identifiers enable malicious eavesdroppers to continuously track users and their movements. In order to prevent such identifier-based tracking, devices could coordinate regular i ...

2013

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

Graph-Constrained Group Testing

Amin Karbasi, Mahdi Cheraghchi Bashi Astaneh, Soheil Mohajerzefreh

Non-adaptive group testing involves grouping arbitrary subsets of

n

items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most

d

d ...

2012

Graph-Constrained Group Testing

Amin Karbasi, Mahdi Cheraghchi Bashi Astaneh, Soheil Mohajerzefreh

Non-adaptive group testing involves grouping arbitrary subsets of

n

items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most

d

d ...

2012