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Source Localization on Graphs via l1 Recovery and Spectral Graph Theory

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The Range of a Random Walk on a Comb

János Pach, Gábor Tardos

The graph obtained from the integer grid Z x Z by the removal of all horizontal edges that do not belong to the x-axis is called a comb. In a random walk on a graph, whenever a walker is at a vertex v, in the next step it will visit one of the neighbors of ...

Electronic Journal Of Combinatorics2013

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

Space crossing numbers

We define the crossing number for an embedding of a graph G into R^3, and prove a lower bound on it which almost implies the classical crossing lemma. We also give sharp bounds on the space crossing numbers of pseudo-random graphs. ...

2011

Semi-Supervised Learning with Spectral Graph Wavelets

Pierre Vandergheynst, David Shuman, Mohammadjavad Faraji

We consider the transductive learning problem when the labels belong to a continuous space. Through the use of spectral graph wavelets, we explore the benefits of multiresolution analysis on a graph constructed from the labeled and unlabeled data. The spec ...

2011

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 and identifying defective items based on tests obtained for each pool. Motivated by applications in network tomography, sensor networks and infection propagati ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

A bipartite strengthening of the Crossing Lemma

János Pach

Let G = (V, E) be a graph with n vertices and m >= 4n edges drawn in the plane. The celebrated Crossing Lemma states that G has at least Omega(m(3)/n(2)) pairs of crossing edges; or equivalently, there is an edge that crosses Omega(m(2)/n(2)) other edges. ...

2010

Towards unifying diffusion and exemplar-based inpainting

Pierre Vandergheynst, Emmanuel D'Angelo

A novel framework for image inpainting is proposed, relying on graph-based diffusion processes. Depending on the construction of the graph, both flow-based and exemplar-based inpainting methods can be implemented by the same equations, hence providing a un ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Degenerate crossing numbers

János Pach

Let G be a graph with n vertices and ea parts per thousand yen4n edges, drawn in the plane in such a way that if two or more edges (arcs) share an interior point p, then they properly cross one another at p. It is shown that the number of crossing points, ...

Springer-Verlag2009

Degree-constrained edge partitioning in graphs arising from discrete tomography

Dominique de Werra, Bernard Ries

Starting from the basic problem of reconstructing a 2-dimensional image given by its projections on two axes, one associates a model of edge coloring in a complete bipartite graph. The complexity of the case with k=3 colors is open. Variations and special ...

2009

Gossiping in a Multi-Channel Radio Network (An Oblivious Approach to Coping With Malicious Interference)

Rachid Guerraoui, Seth Gilbert

We study oblivious deterministic gossip algorithms for multi-channel radio networks with a malicious adversary. In a multi-channel network, each of the n processes in the system must choose, in each round, one of the c channels of the system on which to pa ...

Springer2007

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 and identifying defective items based on tests obtained for each pool. Motivated by applications in network tomography, sensor networks and infection propagati ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010