Call admission problems on trees

We are given nodes in a communication network that request connections to other nodes. A central authority may accept or reject such right away, and once connection is established its duration unbounded edges cannot be used for connections; actions performed without knowledge of future requests, is, we consider an online setting. examine this so-called call admission problem tree networks. The focus on the quality solutions achievable advice setting, when has certain amount information incoming requests. show O(mlog2⁡d) bits additional sufficient algorithm run by perform as well optimal offline algorithm, where m number d largest degree network. In case star network, Ω(mlog2⁡d) also necessary (note d=m). present lower bound complexity small constant competitive ratios whose ratio gradually improves with added 2⌈log2⁡n⌉, n