A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
On the complexity of distributed network decomposition
Journal of Algorithms
Improvements in throughout maximization for real-time scheduling
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Improved Approximation Algorithms for Resource Allocation
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A quasi-PTAS for unsplittable flow on line graphs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Multicommodity demand flow in a tree and packing integer programs
ACM Transactions on Algorithms (TALG)
Fast distributed scheduling via primal-dual
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
A logarithmic approximation for unsplittable flow on line graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices ‹u, v›, along with a profit; the processor wishes to send data between u and v. Towards that goal, the processor needs to select a graph network accessible to it and a path connecting u and v within the selected network. The processor requires exclusive access to the chosen path, in order to route the data. Thus, the processors are competing for routes/channels. A feasible solution selects a subset of demands and schedules each selected demand on a graph network accessible to the processor owning the demand; the solution also specifies the paths to use for this purpose. The requirement is that for any two demands scheduled on the same graph network, their chosen paths must be edge disjoint. The goal is to output a solution having the maximum aggregate profit. Prior work has addressed the above problem in a distibuted setting for the special case where all the graph networks are simply paths (i.e, line-networks). Distributed constant factor approximation algorithms are known for this case. The main contributions of this paper are twofold. First we design a distributed constant factor approximation algorithm for the more general case of tree-networks. The core component of our algorithm is a tree-decomposition technique, which may be of independent interest. Secondly, for the case of line-networks, we improve the known approximation guarantees by a factor of 5. Our algorithms can also handle the capacitated scenario, wherein the demands and edges have bandwidth requirements and capacities, respectively.