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Design of Nonmasking Tree Algorithm

Design of Nonmasking Tree Algorithm. Goal: design a tree construction protocol systematically by constructing its invariant and fault-span. Ideal State. Each process j maintains a variable P.j. P.j denotes the parent of j in the tree. Each process also has a unique ID

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Design of Nonmasking Tree Algorithm

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  1. Design of Nonmasking Tree Algorithm • Goal: design a tree construction protocol systematically by constructing its invariant and fault-span

  2. Ideal State • Each process j maintains a variable P.j. P.j denotes the parent of j in the tree. • Each process also has a unique ID • In an ideal state the graph imposed by the parent relation forms a tree

  3. Faults • Can fail or repair a process • Goal: Reconstruct the tree with the available processes

  4. Due to faults, we may have • Unrooted trees • Because some node’s parent has failed • Multiple (rooted) trees • For example, when a node is repaired, it may form a tree by itself • Observe that there are no cycles. In other words, in the presence of faults, a cycle is not created. • We may want to preserve this during reconstruction. • I.e., this constraint should be in the fault-span

  5. Predicates for Fault-Span (1) • The graph imposed by the parent relation is a forest

  6. Approach for Reconstruction • Dealing with unrooted trees • Somehow the nodes in unrooted trees should be informed so that they know that they are in an unrooted tree • Approach: Introduce a variable color (col) • Green = node thinks it is in rooted tree • Red = node thinks it is in unrooted tree

  7. Action (1) col.j = green (P.j  N.j  col.(P.j) = red)  col.j = red

  8. Predicate in Invariant • What is it that we would like to have true if this action is executed • (P.j  N.j  col.(P.j) = red)  col.j = red

  9. Predicate in Fault-Span (2) • The graph imposed by the parent relation is a forest  • col.j = red  (P.j  N.j  col.(P.j) = red)

  10. Note • Observe that Action (1) is aimed at correcting a predicate in the invariant • Must ensure that during correction, the fault-span constraints are not violated

  11. Predicate in Invariant • (P.j  N.j  col.(P.j) = red)  col.j = red • col.j = green

  12. Action (2) • When should a node set its color to green • Need to ensure that constraints of fault-span are not violated • Need to ensure that constraints of previous predicates in invariant are not violated

  13. Action (2) col.j = red  (????)  col.j = green Choose ???? so that this action does not affect fault-span predicate/previous predicates in invariant

  14. Merging Multiple Trees • Introduce variable root • root.j denotes the ID of the process that j believes to be the root • If a process finds another process with higher root value, it can choose to switch to it.

  15. Action (2) modified col.j = red  (j has no children)  col.j = green, P.j = j, root.j = j

  16. Predicate in Invariant (3) • (P.j  N.j  col.(P.j) = red)  col.j = red • col.j = green • root.j = root.k

  17. Action (3) root.j < root.k  (????)  root.j = root.k, P.j = k

  18. Predicate in Fault-Span • The graph imposed by the parent relation is a forest  • col.j = red  (P.j  N.j  col.(P.j) = red) • col.(P.j) = green  root.j root.(P.j)

  19. Recovery Action for Process Recovery of node j  col.j = red, P.j = j, root.j = j

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