Push-Down Trees: Optimal Self-Adjusting Complete Trees

Chen Avin

doi:10.1109/TNET.2022.3174118

Push-Down Trees: Optimal Self-Adjusting Complete Trees

2022-12-01

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AI

DOI：10.1109/TNET.2022.3174118

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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 is a central building block for more general self-adjusting network designs and 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 \ONRAND 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 \ONDET 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.

Keyword:

Costs

Heuristic algorithms

Servers

Approximation algorithms

Routing

Network topology

Topology

Reconfigurable networks

online algorithms

self-adjusting datastructures

competitive analysis

Push-Down Trees: Optimal Self-Adjusting Complete Trees

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