Distributed Graph Realizations
نویسندگان
چکیده
We study graph realization problems for the first time from a distributed perspective. Graph are encountered in construction of overlay networks that must satisfy certain degree or connectivity properties. them node capacitated clique (NCC) model computing, recently introduced representing peer-to-peer networks. focus on two central variants, degree-sequence realization and minimum threshold-connectivity realization. In sequence problem, each $v$ is associated with notation="LaTeX">$d(v)$ , resulting realizable if it possible to construct an network which . The minimum threshold-connectivity problem requires us satisfies constraints specified between every pair nodes. Overlay realizations can be either explicit implicit. Explicit require both endpoints any edge realized aware edge. implicit realizations, other hand, at least one endpoint needs main algorithms we present following. (Note all our randomized Las Vegas unless otherwise. stated running times hold high probability.) 1) An notation="LaTeX">$\tilde{O}(\min \lbrace \sqrt{m},\Delta \rbrace)$ algorithm sequence. Here, notation="LaTeX">$\Delta = \max _v d(v)$ maximum notation="LaTeX">$m (1/2) \sum number edges final 2) notation="LaTeX">$\tilde{O}(\Delta)$ compute then transform into additional rounds. 3) threshold obtains solution improved notation="LaTeX">$\tilde{O}(1)$ when nodes know other’s IDs. These yield 2-approximations w.r.t. edges. complement upper bounds lower show above tight up factors notation="LaTeX">$\log n$ Additionally, provide realizing trees (including procedure obtaining tree minimal diameter), round approximate finally notation="LaTeX">$O(\log ^2 n)$ non-preassigned case namely, where input may permuted among
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ژورنال
عنوان ژورنال: IEEE Transactions on Parallel and Distributed Systems
سال: 2022
ISSN: ['1045-9219', '1558-2183', '2161-9883']
DOI: https://doi.org/10.1109/tpds.2021.3104239