Self-adjusting Linear Networks with Ladder Demand Graph

Self-adjusting networks (SANs) have the ability to adapt communication demand by dynamically adjusting workload (or demand) embedding, i.e., mapping of requests into network topology. SANs can reduce routing costs for frequently communicating node pairs paying a cost embedding. This is particularly beneficial when has structure, which to. Demand be represented in form graph, defined set nodes (vertices) and pairwise (edges). Thus, adapting interpreted embedding graph challenging both known advance (offline) it revealed edge-by-edge (online). The difficulty also depends on whether we aim at constructing static topology or dynamic (self-adjusting) one that improves as more parts are revealed. Yet very little about these self-adjusting embeddings. In this paper, restricted line ladder $$2\times n$$ grid, including all possible subgraphs ladder. We present an online matches lower bound asymptotically 12-competitive terms request cost. As warm up result, optimal algorithm cycle graph. oracle-based arbitrary constant overhead.