Fractal Prefetching B+-Trees: Optimizing Both Cache and Disk - - PowerPoint PPT Presentation
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion Fractal Prefetching B+-Trees: Optimizing Both Cache and Disk Performance Shimin Chen, Phillip B. Gibbons, Todd C. Mowry, and Gary Valentin October 3,
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Shimin Chen, Phillip B. Gibbons, Todd C. Mowry, and Gary Valentin October 3, 2011 Presenter: Mike Qin mikeandmore@gmail.com
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Large page size optimize the I/O, results in binary search in a huge page to CPU cache.
Binary Search is not cache friendly.
compare compare compare bingo
Small page size will slow down search for disk I/O.
search bingo search search bingo
2 seeks 4 seeks
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Optimize both disk I/O and cache utilization – put a subtree in the tree node.
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Multiple page node size
Prefetch more data that have spacial locality.
Storage system can strip a page accross several disks. Read ahead
Better Page Replacement Policy
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Single disk page as a node
doesn’t exists. Read ahead for range-scans. Overlap the I/O cache miss.
1 Find the start and end range query. 2 Prefetch the page far-away from the begining page. range start range end prefetching from this block
Tree
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Micro-indexing
An extra array for indexing. All fits into one node.
Cache friendly at the page level
Tree with in a tree node (a page).
Merge part of the tree into several pages.
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
A single node contains a complete sub-tree. It yeilds out fixed amount (N-2N)
merge. But wait... How about the space usage of each page?
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Given the fixed amount of fan-outs of each subtree, the space usage is not deterministic!
Overflow!
page
very sparse subnode
page
Space Wasted
very dense subnode
Overflow Underflow
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Insert:
1 Find a node to insert in the page 2 Find a slot, if not, split the node 3 If no room for another node, reorganized the subtree. 4 If still no room, split the whole page.
Delete:
1 Find the elements in the page to delete. 2 Mark that as empty slot. (Don’t merge the node on half empty.) 3 If page fan-out smaller than minimum fan-out. Merge the page. 4 Reorganized the tree if underflow.
Bulkload:
1 Compute the level according to fan-out. 2 Organized the subtree as sparse as possible.
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Page Cache Fetch Cost T1 CPU Cache Fetch Cost Tnext Number of cache lines of non-leaf nodes w Number of cache lines of leaf-nodes x Level of subtree L Cost = (L − 1) × NonLeafCost + LeafCost = (L − 1) × [T1 + (w − 1)Tnext] + [T1 + (x − 1)Tnext] As fan-out gets larger, cost also gets larger. Our goal: largest fan-out with < 10% larger than optimal cost.
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Merge the fine-grained node into pages. Stratagy:
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Merge the fine-grained node into pages. Stratagy:
leaf node placement noleaf node placement Overflowed leaf node parent
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Leaf node:
1 Find a slot to insert. 2 If full, split the node. 3 If no space for a new node, split the whole page.
Leaf parent node:
1 Find a slot to insert. 2 If full, split the node. 3 If no space for new node and parent of this node also need to be split, then
split the parent and this node. Put them in the same page.
4 Otherwise, allocate space from overflow pages.
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Nonleaf Node:
1 Find a slot to insert. 2 If full, split the node. 3 If no space for new node. Reorganize the subtree within this page. 4 If still no space, split the page.
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
insert
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
split?
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
split!
space efficiency problem
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Page size:
cost
Buffer manager:
Comparison:
Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Search on 100% bulkloaded initialization.
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1 1.5 2 2.5 3 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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1 1.5 2 2.5 3 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´µ Ô ×Þ10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) nonleaf= 64B nonleaf=128B nonleaf=192B(selected) nonleaf=256B nonleaf=320B nonleaf=384B nonleaf=448B nonleaf=512B 10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) 128B 256B 512B 704B(selected) 1024B Best Synthesized
´µ ×¹¬Ö×Ø Ô60 70 80 90 100 1.5 2 2.5 3 3.5 bulkload factor when building the trees execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
ÙÖ ½¾ ËÖ60 70 80 90 100 10 20 30 40 50 60 70 80 bulkload factor (16KB page) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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10 20 30 40 50 60 70 # of entries in leaf pages (16KB page, 100% full) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´µ Î ÖÝÒ ÙÐÐÓ ØÓÖ× ´µ Î ÖÝÒ10 20 30 40 50 60 70 80 90 (3M entries in leaf pages, 100% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 20 40 60 80 100 (3M entries in leaf pages, 70% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´ µ Î ÖÝÒ Ô ×Þ× ´½¼¼± ÙÐе ´µ Î ÖÝÒ Ô ×Þ× ´¼± ÙÐе ÙÖ ½¿ ÁÒ×ÖØÓÒ Ô ÖÓÖÑÒ ÜÔ ÖÑÒ Ø× Ò ØÖÓÖ ×ÑÐÖ Ô ÖÓÖÑÒ º Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Search on 100% bulkloaded initialization.
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1 1.5 2 2.5 3 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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1 1.5 2 2.5 3 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´µ Ô ×Þ10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´ µ Ô ×Þ10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) nonleaf= 64B nonleaf=128B nonleaf=192B(selected) nonleaf=256B nonleaf=320B nonleaf=384B nonleaf=448B nonleaf=512B 10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) 128B 256B 512B 704B(selected) 1024B Best Synthesized
´µ ×¹¬Ö×Ø Ô60 70 80 90 100 1.5 2 2.5 3 3.5 bulkload factor when building the trees execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
ÙÖ ½¾ ËÖ60 70 80 90 100 10 20 30 40 50 60 70 80 bulkload factor (16KB page) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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10 20 30 40 50 60 70 # of entries in leaf pages (16KB page, 100% full) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´µ Î ÖÝÒ ÙÐÐÓ ØÓÖ× ´µ Î ÖÝÒ10 20 30 40 50 60 70 80 90 (3M entries in leaf pages, 100% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 20 40 60 80 100 (3M entries in leaf pages, 70% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´ µ Î ÖÝÒ Ô ×Þ× ´½¼¼± ÙÐе ´µ Î ÖÝÒ Ô ×Þ× ´¼± ÙÐе ÙÖ ½¿ ÁÒ×ÖØÓÒ Ô ÖÓÖÑÒ ÜÔ ÖÑÒ Ø× Ò ØÖÓÖ ×ÑÐÖ Ô ÖÓÖÑÒ º Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Search on a varied bulkloaded initialization.
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1 1.5 2 2.5 3 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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1 1.5 2 2.5 3 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) nonleaf= 64B nonleaf=128B nonleaf=192B(selected) nonleaf=256B nonleaf=320B nonleaf=384B nonleaf=448B nonleaf=512B 10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) 128B 256B 512B 704B(selected) 1024B Best Synthesized
´µ ×¹¬Ö×Ø Ô60 70 80 90 100 1.5 2 2.5 3 3.5 bulkload factor when building the trees execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
ÙÖ ½¾ ËÖ60 70 80 90 100 10 20 30 40 50 60 70 80 bulkload factor (16KB page) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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10 20 30 40 50 60 70 # of entries in leaf pages (16KB page, 100% full) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´µ Î ÖÝÒ ÙÐÐÓ ØÓÖ× ´µ Î ÖÝÒ10 20 30 40 50 60 70 80 90 (3M entries in leaf pages, 100% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 20 40 60 80 100 (3M entries in leaf pages, 70% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´ µ Î ÖÝÒ Ô ×Þ× ´½¼¼± ÙÐе ´µ Î ÖÝÒ Ô ×Þ× ´¼± ÙÐе ÙÖ ½¿ ÁÒ×ÖØÓÒ Ô ÖÓÖÑÒ ÜÔ ÖÑÒ Ø× Ò ØÖÓÖ ×ÑÐÖ Ô ÖÓÖÑÒ º Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Insert performance under a) different bulkload factors b) # of entries.
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1 1.5 2 2.5 3 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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1 1.5 2 2.5 3 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) nonleaf= 64B nonleaf=128B nonleaf=192B(selected) nonleaf=256B nonleaf=320B nonleaf=384B nonleaf=448B nonleaf=512B 10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) 128B 256B 512B 704B(selected) 1024B Best Synthesized
´µ ×¹¬Ö×Ø Ô60 70 80 90 100 1.5 2 2.5 3 3.5 bulkload factor when building the trees execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
ÙÖ ½¾ ËÖ60 70 80 90 100 10 20 30 40 50 60 70 80 bulkload factor (16KB page) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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10 20 30 40 50 60 70 # of entries in leaf pages (16KB page, 100% full) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´µ Î ÖÝÒ ÙÐÐÓ ØÓÖ× ´µ Î ÖÝÒ10 20 30 40 50 60 70 80 90 (3M entries in leaf pages, 100% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 20 40 60 80 100 (3M entries in leaf pages, 70% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´ µ Î ÖÝÒ Ô ×Þ× ´½¼¼± ÙÐе ´µ Î ÖÝÒ Ô ×Þ× ´¼± ÙÐе ÙÖ ½¿ ÁÒ×ÖØÓÒ Ô ÖÓÖÑÒ ÜÔ ÖÑÒ Ø× Ò ØÖÓÖ ×ÑÐÖ Ô ÖÓÖÑÒ º Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Insert performance under different page size. c) 100% full d) 70% full
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1 1.5 2 2.5 3 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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1 1.5 2 2.5 3 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) nonleaf= 64B nonleaf=128B nonleaf=192B(selected) nonleaf=256B nonleaf=320B nonleaf=384B nonleaf=448B nonleaf=512B 10
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1 1.5 2 2.5 3 3.5 # of entries in leaf pages execution time (M cycles) 128B 256B 512B 704B(selected) 1024B Best Synthesized
´µ ×¹¬Ö×Ø Ô60 70 80 90 100 1.5 2 2.5 3 3.5 bulkload factor when building the trees execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
ÙÖ ½¾ ËÖ60 70 80 90 100 10 20 30 40 50 60 70 80 bulkload factor (16KB page) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10
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10 20 30 40 50 60 70 # of entries in leaf pages (16KB page, 100% full) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´µ Î ÖÝÒ ÙÐÐÓ ØÓÖ× ´µ Î ÖÝÒ10 20 30 40 50 60 70 80 90 (3M entries in leaf pages, 100% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 20 40 60 80 100 (3M entries in leaf pages, 70% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´ µ Î ÖÝÒ Ô ×Þ× ´½¼¼± ÙÐе ´µ Î ÖÝÒ Ô ×Þ× ´¼± ÙÐе ÙÖ ½¿ ÁÒ×ÖØÓÒ Ô ÖÓÖÑÒ ÜÔ ÖÑÒ Ø× Ò ØÖÓÖ ×ÑÐÖ Ô ÖÓÖÑÒ º Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
Delete performance under different a) bulkload factors b) page sizes.
60 70 80 90 100 5 10 15 20 25 30 bulkload factor (16KB page) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10 20 30 40 50 (3M entries in leaf pages, 100% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´µ Î ÖÝÒ ÙÐÐÓ ØÓÖ× ´µ Î ÖÝÒ Ô ×Þ× ´½¼¼± ÙÐе ÙÖ ½ ÐØÓÒ Ô ÖÓÖÑÒ ×¹ÓÔØÑÞ200 400 600 800 1000 1200 simulation time (M cycles) Disk−optimized B+tree Disk−first fpB+tree Cache−first fpB+tree
ÙÖ ½ ÊÒ × Ò Ô ÖÓÖÑÒ ´½Ã Ô¸ × ÒÒÒ ½Å10 20 30 40 50 page size space overhead (percentage) 4KB 8KB 16KB 32KB Disk−first fpB+tree Cache−first fpB+tree 10 20 30 40 50 page size space overhead (percentage) 4KB 8KB 16KB 32KB Disk−first fpB+tree Cache−first fpB+tree
´µ ØÖ ÙÐÐÓÒ ØÖ× ½¼¼± ÙÐÐ ´µ ÅØÙÖ ØÖ× ÙÖ ½ ËÔ Ó Ú Ö Ü׺ Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
60 70 80 90 100 5 10 15 20 25 30 bulkload factor (16KB page) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10 20 30 40 50 (3M entries in leaf pages, 100% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´µ Î ÖÝÒ ÙÐÐÓ ØÓÖ× ´µ Î ÖÝÒ Ô ×Þ× ´½¼¼± ÙÐе ÙÖ ½ ÐØÓÒ Ô ÖÓÖÑÒ ×¹ÓÔØÑÞ200 400 600 800 1000 1200 simulation time (M cycles) Disk−optimized B+tree Disk−first fpB+tree Cache−first fpB+tree
ÙÖ ½ ÊÒ × Ò Ô ÖÓÖÑÒ ´½Ã Ô¸ × ÒÒÒ ½Å10 20 30 40 50 page size space overhead (percentage) 4KB 8KB 16KB 32KB Disk−first fpB+tree Cache−first fpB+tree 10 20 30 40 50 page size space overhead (percentage) 4KB 8KB 16KB 32KB Disk−first fpB+tree Cache−first fpB+tree
´µ ØÖ ÙÐÐÓÒ ØÖ× ½¼¼± ÙÐÐ ´µ ÅØÙÖ ØÖ× ÙÖ ½ ËÔ Ó Ú Ö Ü׺ Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
a) Bulkload 10M keys. b) Insert 9M keys and bulkload 1M keys.
60 70 80 90 100 5 10 15 20 25 30 bulkload factor (16KB page) execution time (M cycles) Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree 10 20 30 40 50 (3M entries in leaf pages, 100% full) execution time (M cycles) 4KB 8KB 16KB 32KB Disk−optimized B+tree Micro−indexing Disk−first fpB+tree Cache−first fpB+tree
´µ Î ÖÝÒ ÙÐÐÓ ØÓÖ× ´µ Î ÖÝÒ Ô ×Þ× ´½¼¼± ÙÐе ÙÖ ½ ÐØÓÒ Ô ÖÓÖÑÒ ×¹ÓÔØÑÞ200 400 600 800 1000 1200 simulation time (M cycles) Disk−optimized B+tree Disk−first fpB+tree Cache−first fpB+tree
ÙÖ ½ ÊÒ × Ò Ô ÖÓÖÑÒ ´½Ã Ô¸ × ÒÒÒ ½Å10 20 30 40 50 page size space overhead (percentage) 4KB 8KB 16KB 32KB Disk−first fpB+tree Cache−first fpB+tree 10 20 30 40 50 page size space overhead (percentage) 4KB 8KB 16KB 32KB Disk−first fpB+tree Cache−first fpB+tree
´µ ØÖ ÙÐÐÓÒ ØÖ× ½¼¼± ÙÐÐ ´µ ÅØÙÖ ØÖ× ÙÖ ½ ËÔ Ó Ú Ö Ü׺ Introduction Optimizing I/O Performance Optimizing Cache Performance Evaluation Discussion
anyway.
grain?