分布式算法课件5.ppt

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分布式算法课件5

Interference among concurrent MWOE searches Suppose C gets absorbed into C′ via an edge from i to j, while C′ is working on determining its MWOE. Two cases: j has not yet reported its local mwoe when the absorb occurs. Then it’s not too late to include C in the search for the MWOE of C′. So j forwards the initiate message into C. j has already reported its local mwoe. Then it’s too late to include C in the search. But it doesn’t matter: the MWOE for the combined component can’t be outgoing from a node in C anyhow! * A few details Specific messages: initiate:Broadcast from leader to find MWOE; piggybacks component name. report: Convergecast MWOE responses back to leader. test:Asks whether an edge is outgoing from the component. accept/reject:Answers. changeroot: Sent from leader to endpoint of MWOE. connect: Sent across the MWOE, to connect components. We say merge occurs when connect message has been sent both ways on the edge (2 nodes must have same level). We say absorb occurs when connect message has been sent on the edge from a lower-level to a higher-level node. * Test-Accept-Reject protocol Bookkeeping: Each process i keeps a list of incident edges in order of weight, classified as: branch(in the MST), rejected(leads to same component), or unknown(not yet classified). * Test-Accept-Reject protocol Process i tests only unknown edges, sequentially in order of weight: Sends test message, with (core, level); recipient j compares. If same (core, level), j sends reject(same component), and i reclassifies edge as rejected. If (core, level) pairs are unequal and level(j) ≥level(i) then j sends accept (different component). i does not reclassify the edge. If level(j) level(i) then j delays responding, until level(j) ≥level(i). Retesting is possible, for accepted edges. Reclassify edge as branch as a result of changeroot message. * Complexity As for synchronous version. Messages: O(|E| + n log n) 4|E| for test-reject msgs(one pair for each direction of every edge) n

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