Arboricity and subgraph listing algorithms
SIAM Journal on Computing
Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Forests, frames, and games: algorithms for matroid sums and applications
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Planar orientations with low out-degree and compaction of adjacency matrices
Theoretical Computer Science
The design and analysis of algorithms
The design and analysis of algorithms
Arboricity and bipartite subgraph listing algorithms
Information Processing Letters
Journal of the ACM (JACM)
Efficient computation of implicit representations of sparse graphs
Discrete Applied Mathematics
Dynamic Representation of Sparse Graphs
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Greedy approximation algorithms for finding dense components in a graph
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Short path queries in planar graphs in constant time
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Beyond the flow decomposition barrier
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Finding a Maximum Density Subgraph
Finding a Maximum Density Subgraph
All maximal independent sets and dynamic dominance for sparse graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Upper degree-constrained partial orientations
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Graph classes and the complexity of the graph orientation minimizing the maximum weighted outdegree
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
Approximation Algorithms for the Graph Orientation Minimizing the Maximum Weighted Outdegree
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Improved induced matchings in sparse graphs
Discrete Applied Mathematics
Graph classes and the complexity of the graph orientation minimizing the maximum weighted outdegree
Discrete Applied Mathematics
Approximation algorithms for the graph orientation minimizing the maximum weighted outdegree
Journal of Combinatorial Optimization
Upper and lower degree bounded graph orientation with minimum penalty
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
The complexity of the proper orientation number
Information Processing Letters
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We deal with the problem of finding such an orientation of a given graph that the largest number of edges leaving a vertex (called the outdegree of the orientation) is small. For any ε∈(0,1) we show an $\tilde{O}(|E(G)|/\varepsilon)$ time algorithm which finds an orientation of an input graph G with outdegree at most ⌈(1+ε)d*⌉, where d* is the maximum density of a subgraph of G. It is known that the optimal value of orientation outdegree is ⌈d* ⌉. Our algorithm has applications in constructing labeling schemes, introduced by Kannan et al. in [18] and in approximating such graph density measures as arboricity, pseudoarboricity and maximum density. Our results improve over the previous, 2-approximation algorithms by Aichholzer et al. [1] (for orientation / pseudoarboricity), by Arikati et al. [3] (for arboricity) and by Charikar [5] (for maximum density).