Paper detail

A Paradigm for Channel Assignment and Data Migration in Distributed Systems

In this manuscript, we consider the problems of channel assignment in wireless networks and data migration in heterogeneous storage systems. We show that a soft edge coloring approach to both problems gives rigorous approximation guarantees. In the channel assignment problem arising in wireless networks a pair of edges incident to a vertex are said to be conflicting if the channels assigned to them are the same. Our goal is to assign channels (color edges) so that the number of conflicts is minimized. The problem is NP-hard by a reduction from Edge coloring and we present two combinatorial algorithms for this case. The first algorithm is based on a distributed greedy method and gives a solution with at most $2(1-\frac{1}{k})|E|$ more conflicts than the optimal solution.The approximation ratio if the second algorithm is $1 + \frac{|V|}{|E|}$, which gives a ($1 + o(1)$)-factor for dense graphs and is the best possible unless P = NP. We also consider the data migration problem in heterogeneous storage systems. In such systems, data layouts may need to be reconfigured over time for load balancing or in the event of system failure/upgrades. It is critical to migrate data to their target locations as quickly as possible to obtain the best performance of the system. Most of the previous results on data migration assume that each storage node can perform only one data transfer at a time. However, storage devices tend to have heterogeneous capabilities as devices may be added over time due to storage demand increase. We develop algorithms to minimize the data migration time. We show that it is possible to find an optimal migration schedule when all $c_v$'s are even. Furthermore, though the problem is NP-hard in general, we give an efficient soft edge coloring algorithm that offers a rigorous $(1 + o(1))$-approximation guarantee.