2,799 research outputs found
Euclidean Greedy Drawings of Trees
Greedy embedding (or drawing) is a simple and efficient strategy to route
messages in wireless sensor networks. For each source-destination pair of nodes
s, t in a greedy embedding there is always a neighbor u of s that is closer to
t according to some distance metric. The existence of greedy embeddings in the
Euclidean plane R^2 is known for certain graph classes such as 3-connected
planar graphs. We completely characterize the trees that admit a greedy
embedding in R^2. This answers a question by Angelini et al. (Graph Drawing
2009) and is a further step in characterizing the graphs that admit Euclidean
greedy embeddings.Comment: Expanded version of a paper to appear in the 21st European Symposium
on Algorithms (ESA 2013). 24 pages, 20 figure
External-Memory Network Analysis Algorithms for Naturally Sparse Graphs
In this paper, we present a number of network-analysis algorithms in the
external-memory model. We focus on methods for large naturally sparse graphs,
that is, n-vertex graphs that have O(n) edges and are structured so that this
sparsity property holds for any subgraph of such a graph. We give efficient
external-memory algorithms for the following problems for such graphs: -
Finding an approximate d-degeneracy ordering; - Finding a cycle of length
exactly c; - Enumerating all maximal cliques. Such problems are of interest,
for example, in the analysis of social networks, where they are used to study
network cohesion.Comment: 23 pages, 2 figures. To appear at the 19th Annual European Symposium
on Algorithms (ESA 2011
How the Experts Algorithm Can Help Solve LPs Online
We consider the problem of solving packing/covering LPs online, when the
columns of the constraint matrix are presented in random order. This problem
has received much attention and the main focus is to figure out how large the
right-hand sides of the LPs have to be (compared to the entries on the
left-hand side of the constraints) to allow -approximations
online. It is known that the right-hand sides have to be times the left-hand sides, where is the number of constraints.
In this paper we give a primal-dual algorithm that achieve this bound for
mixed packing/covering LPs. Our algorithms construct dual solutions using a
regret-minimizing online learning algorithm in a black-box fashion, and use
them to construct primal solutions. The adversarial guarantee that holds for
the constructed duals helps us to take care of most of the correlations that
arise in the algorithm; the remaining correlations are handled via martingale
concentration and maximal inequalities. These ideas lead to conceptually simple
and modular algorithms, which we hope will be useful in other contexts.Comment: An extended abstract appears in the 22nd European Symposium on
Algorithms (ESA 2014
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