NOTE ON THE OUTDEGREE OF A NODE IN RANDOM RECURSIVE TREES

  • Published : 2003.09.01

Abstract

In this note we find the exact Probability distribution of d$\_$n, i/ the outdegree of the node i, in a random recursive tree with n nodes. For i = i$\_$n/ increasing as a linear function on n, we show that d$\_$n/,i$\_$n/ is asymptotically normal.

Keywords

References

  1. Random Structures and Algorithms v.5 Random Recursive Forests K.T.Balinska;L.V.Quintas;J.Szymanski
  2. Graphs and hypergraphs C.Berge
  3. Acta Informatica v.26 Applications of the theory of records in the study of random trees L.Devroye
  4. Operations Research v.32 Two probability models of pyramids or chain letter schemes demonstrating that their promotional calims are unreliable J.Gastwirth;P.Bhattacharya
  5. Random Structures and Algorithms v.3 Asymptotic joint formality of outdegrees of nodes in random recursive trees H.Mahmoud;R.Smythe
  6. London Math. Soc. Lecture Notes v.13 The distance between nodes in recursive trees J.Moon
  7. J. Applied Prob. v.19 On the number of terminal vertices in certain random trees with on application to stemma construction in philology D.Najock;C.Heyde
  8. Theor. Probability and Math. Statist. v.51 A survey of recursive trees R.T.Smythe;H.M.Mahmoud
  9. Korean J. Comput. & Appl. Math. v.6 no.3 An optimal algorithm for finding depth-first spanning tree on permutation graphs Sukumar Mondal;Modhumangal Pal;Tapan K.Pal
  10. Korean J. Comput. & Appl. Math. v.5 no.2 A new parallel algorithm for rooting a tree Taenam Kim;Dukwan Oh;Eunki Lim