heap - Complexity in Dijkstras algorithm -



heap - Complexity in Dijkstras algorithm -

so i've been attempting analyze specialized variant of dijkstras algorithm i've been working on. i'm after worst case complexity.

the algorithm uses fibonacci heap in case of normal dijkstra run in o(e + v log v).

however implementation needs lookup in inner loop update neighbours. lookup execute every border , in logarithmic time, lookup in datastructure contains edges. graph has restriction no node have more 4 neighbours.

o(vlog v) complexity outer loop i'm not sure worst case inner loop. i'm thinking since each border in graph checked o(e) times , each border take logarithmic time should elog e should exceed vlog v , result in o(elog e) complexity algorithm.

any insight awesome!

the amortized complexity of decrease-key on fibonacci heap o(1), have |e| such operations on fibonacci heap, total cost o(e). have |v| extract-min operations, cost o(lnv) each. total cost o(e+vlnv).

heap complexity-theory dijkstra

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