Dynamic TCP acknowledgment in the LogP model

When messages, which are to be sent point-to-point in a network, become available at irregular intervals, a decision must be made each time a new message becomes available as to whether it should be sent immediately or if it is better to wait for more messages and send them all together. Because of physical properties of the networks, a certain minimum amount of time must elapse in between the transmission of two packets. Thus, whereas waiting delays the transmission of the current data, sending immediately may delay the transmission of the next data to become available even more. We propose a new quality measure and derive optimal deterministic and randomized algorithms for this on-line problem.     

The k-Client Problem

Virtually all previous research in online algorithms has focused on single-threaded systems where only a single sequence of requests compete for system resources. To model multithreaded online systems, we define and analyze the k-client problem, a dual of the well-studied k-server problem. In the basic k-client problem, there is a single server and k clients, each of which generates a sequence of requests for service in a metric space. The crux of the problem is deciding which client's request the single server should service rather than which server should be used to service the current request. We also consider variations where requests have nonzero processing times and where there are multiple servers as well as multiple clients.We evaluate the performance of algorithms using several cost functions including maximum completion time and average completion time. Two of the main results we derive are tight bounds on the performance of several commonly studied disk scheduling algorithms and lower bounds of on the competitive ratio of any online algorithm for the maximum completion time and average completion time cost functions when k is a power of 2. Most of our results are essentially identical for the maximum completion time and average completion time cost functions.