Abstract:
This paper studies a fundamental algorithmic problem related to the design of demand-aware networks: networks whose topologies adjust toward the traffic patterns they serve, in an online manner. The goal is to strike a tradeoff between the benefits of such adjustments (shorter routes) and their costs (reconfigurations). In particular,
we consider the problem of designing a self-adjusting tree network which
serves single-source, multi-destination communication. The problem has
interesting connections to self-adjusting datastructures. We present two
constant-competitive online algorithms for this problem, one randomized and one deterministic. Our approach is based on a natural notion
of Most Recently Used (MRU) tree, maintaining a working set. We prove
that the working set is a cost lower bound for any online algorithm, and
then present a randomized algorithm Random-Push which approximates
such an MRU tree at low cost, by pushing less recently used communication partners down the tree, along a random walk. Our deterministic
algorithm Move-Half does not directly maintain an MRU tree, but its
cost is still proportional to the cost of an MRU tree, and also matches
the working set lower bound.
