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# 11-2 notes - An algorithmic event of input size n occurs...

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An algorithmic event of input size n occurs “with high probability” (WHP) if , , such that Pr(one pillar has height > C*log(n)) = (1/2) clog(n) = Pr(max of n pillars has height > c * log(n) ) = Pr(max of n pillars has height > c * log(n) ) ^^^AKA Given Disk-Bound Computation We have – CPU, memory, disk CPU is arbitrarily fast compared to disk, memory is arbitrarily fast but small Disk is big, but read/write is slow o Can only read/write one block at a time Storage Speed Size L2/L3 Cache 5-15 ns ~10 7 bytes DRAM 30-50 ns ~10 10 bytes Disk 4-8 ms (4-8*10 6 ns) ~10 12 bytes (& up) Runtime of algorithm is measured in # of disk ops (reads and writes) Disk-based Tree Each node can hold a variable # of keys If node y has n(x) keys, it has n(x)+1 children # of keys/node has some max m o <= m+1 children/node M / \ OH QTX / | \ / | | \ BC FG JKL NP RS VW YZ Pick m such that each node fits in one disk block To access node x o Disk-read(x) o Disk-write(x) Suppose one block can store 999 keys o How many keys can fit in a tree of height 3?

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11-2 notes - An algorithmic event of input size n occurs...

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