in a distributed network of processors sharing one indivisible memory page of size D. During runtime,

the processors access a unit of data from the page, and the system is allowed to migrate the page

between the processors. The problem is to compute (on-line) a schedule of page movements

to minimize the total communication cost.

The Dynamic Page Migration problem is an extension to the page migration.

It attempts to model the network dynamics, occurring, for example, in mobile networks.

However, the pace of changes is restricted, i.e. the distances between processors can

change only by a constant per round.

The movement of the nodes induce changes in the communication cost between each pair of nodes,

which is proportional to the distance between them raised to some power $alpha$.

This is typical for mobile wireless networks, where nodes can move with a constant speed,

and the cost of communication is measured in terms of energy used for sending the data.

Thus, by setting $alpha$ equal to the propagation exponent of the medium,

cost minimization becomes minimizing the total energy consumption in the system.

However, as proven in citedynamic-page-migration, if both network mobility and

request sequence are created by an adversary, then the competitive ratio is polynomially large in D and

in the number of the nodes. In our search for a reasonable, close-to-reality model, in this paper we

consider a scenario in which the network mobility is adversarial, but the requests are

generated randomly by a stochastic process. We design an algorithm MTFR for this scenario,

and prove that it is O(1)-competitive, on expectation and with high probability. AU - Bienkowski, Marcin ID - 18917 T2 - Proc. of the 17th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2005) TI - Dynamic Page Migration with Stochastic Requests ER - TY - CONF AB - We consider Dynamic Page Migration (DPM) problem, one of the fundamental subproblems of data management in dynamically changing networks. We investigate a hybrid scenario, where access patterns to the shared object are dictated by an adversary, and each processor performs a random walk in X. We extend the previous results of [4]: we develop algorithms for the case where X is a ring, and prove that with high probability they achieve a competitive ratio of O~(min{D−−√4,n}), where D is the size of the shared object and n is the number of nodes in the network. These results hold also for any d-dimensional torus or mesh with diameter at least Ω~(D−−√). AU - Bienkowski, Marcin AU - Korzeniowski, Miroslaw ID - 18912 SN - 0302-9743 T2 - Proc. of the European Conference in Parallel Processing (Euro-Par) TI - Dynamic Page Migration Under Brownian Motion ER -