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Topic: Radix tree

	Trees I: Radix trees [LWN.net]
		A Linux radix tree is a mechanism by which a (pointer) value can be associated with a (long) integer key.
		Nick Piggin currently has a patch circulating which would use read-copy-update to free tree nodes; this patch would allow lookup operations to be performed without locking as long as (1) the resulting pointer is only used in atomic context, and (2) the calling code avoids creating race conditions of its own.
		In practice, deleting all items from a radix tree will free all memory associated with it other than the root node, which can then be disposed of normally.
	lwn.net /Articles/175432 (1409 words)

	py-radix - radix tree data structure for Python
		This is a Python equivalent to Dave Plonka's Perl Net::Patricia (it even steals the same radix tree code from MRTd).
		The radix tree (a.k.a Patricia tree) is the data structure most commonly used for routing table lookups.
		The underlying radix tree implementation is taken (and modified) from MRTd and is subject to a 4-term BSD license.
	www.mindrot.org /projects/py-radix (311 words)

	Dictionary (Radix Tree) (Site not responding. Last check: )
		The DSA library manages the dynamic memory requests, of which there are plenty: the radix tree is kept as tight as possible all the time, removing superfluous internal nodes by coalescing them if possible, and by creating nodes only when inavoidably needed.
		Within the memory area dedicated to the dictionary and maintained by the DSA, the DIC library establishes a Radix Tree to keep the nodes of the provided entries such, that the tree integrity is never compromised.
		The Radix Tree is kept as tight as possible during all these operations.
	herbert.gandraxa.com /herbert/dic.asp (1798 words)

	Radix tree
		A radix tree, Patricia trie/tree, or crit bit tree is a specialized set data structure based on the trie that is used to store a set of strings.
		The radix tree is easiest to understand as a space-optimized tree where each node with only one child is merged with its child.
		Radix trees also share the disadvantages of tries, however: as they can only be applied to strings of elements or elements with a reversible mapping (bijection) to strings, they lack the full generality of balanced search trees, which apply efficiently to any datatype with a total ordering (for example, floating-point numbers).
	erwiki.com /article/Patricia_trie (793 words)

	Structures - abstraction and implementation (Site not responding. Last check: )
		Radix search: use the binary representation of the keys and compare the bits one by one until a difference is found.
		Radix trees are used when the keys are long.
		The height of the tree is limited by the number of the bits in the keys.
	faculty.simpson.edu /lydia.sinapova/www/cmsc250-01/L09-AVLRadix.htm (1521 words)

	RadixTree (Scalable Simulation Framework)
		Examines each node in the tree which is associated with a proper prefix of the given binary string, and finds all of the ones which have (non-null) data associated with them.
		Examines each node in the tree which is associated with a proper prefix of the given binary string, and finds the shortest one which has (non-null) data associated with it.
		Examines each node in the tree which is associated with a proper prefix of the given binary string, and finds the longest one which has (non-null) data associated with it.
	www.ssfnet.org /javadoc/SSF/OS/BGP4/Util/RadixTree.html (815 words)

	[No title]
		Radix Search Tree Files: rst.c, rst.h The radix search tree is the similar to the digital search tree.
		However, in a radix search tree, all data items are stored as leaves in the tree, and the internal nodes of the tree have no key.
		However, unlike the digital search tree, the radix search tree does not need to spend a key comparison at each node that is traversed in the search.
	www.cosc.canterbury.ac.nz /research/RG/alg/rst.txt (1214 words)

	tst() (Site not responding. Last check: )
		A radix tree is an R-way tree where R is the size of the character set used in the key.
		Radix tree searches are very fast because the number of operations to find an entry is independant of the number of entries in the tree.
		The problem with a radix tree is that although the search time is constant with respect to the number of entries (N) and linear with respect to the key size(L) the space used is O(R * L)].
	www.siue.edu /~cbwilso/dale/doc/tst/package-summary.html (863 words)

	Radix tree (Site not responding. Last check: )
		Sometimes the names radix tree and crit bit tree are only applied to trees storing integers and Patricia trie is retained for more general inputs, but the structure works the same in all cases.
		The radix tree is easiest to understand as a space-optimized trie where each node with only one child is merged with its child.
		Radix trees also share the disadvantages of tries, however: as they can only be applied to strings of elements or elements with a reversible mapping (bijection) to strings, they lack the full generality of balanced search trees, which apply efficiently to any datatype with a total ordering (for example, floating-point numbers).
	www.dejavu.org /cgi-bin/get.cgi?ver=93&url=http://articles.gourt.com/%22http%3A%2F%2Farticles.gourt.com%2F%3Farticle%3DPatricia (870 words)

	Eazy's Radix Paper
		The radix sort was implemented back in the days where they used to use punch cards to input data.
		Tree sorting is good because unless the data has been given sorted already the Big-O will be less than n^2.
		Radix sort doesn't do any comparison even though it needs to pass over a set of data more than once, it still retains worst case O(n) because the number of bins and times passed is dependant on the data that's being sorted.
	www2.hawaii.edu /~eshimane/ics211/Algorithm/RadixSort.htm (824 words)

	Re: [patch 5/7] radix-tree: lockless readside
		My first guess is that > it protects the pointers and internal nodes of the > radix tree, but not the objects in the leaves of the > trees (in other words, the things pointed to by the > return value from things like radix_tree_lookup_slot()).
		Indeed we are protecting the internal nodes of the radix tree, however the speculative get operation needs to dereference a pointer to the page.
		One thing we could do differently is this: instead of receiving a pointer to the struct page from the radix tree lookup, we could actually do as you say and push the rcu locking into the radix tree lookup.
	lists.zerezo.com /linux-kernel/msg30364.html (507 words)

	A Tree-Based Packet Routing Table for Berkeley Unix
		The collection of prototype addresses are assembled into a variant of a PATRICIA tree, which is technically a binary radix tree with one-way branching removed.
		The test results show the new (radix tree based) method to be about 50% faster in constructing the tree and 200% faster in searching it.
		We include a somewhat simplified version of the header file for the radix tree; but the algorithm for searching the tree is taken verbatim.
	homepage.fcgnetworks.net /gated/config_guide/radix.html (4032 words)

	[No title] (Site not responding. Last check: )
		An Improved Radix Tree for Routing Tables Bharat Madan IBM Corp. Abstract: Routing is an important issue in intra and inter working.
		'Radix tree' is a binary tree which has been used to implement the routing table.
		For a large network with many sub-nets may result in a radix tree which is deep and a result back tracking which is expensive in terms of time.
	www.cs.odu.edu /%7Eibl/public/colloquium/spring97/Madan.txt (221 words)

	Linux Kernel Documentation :: prio_tree.txt
		For example, 33 in figure we have 3 overflow-sub-trees corresponding to radix indices 34 0, 2, and 4.
		35 36 In the final tree the first few (prio_tree_root->index_bits) levels 37 are indexed using heap and radix indices whereas the overflow-sub-trees below 38 those levels (i.e.
		79 Whenever index_bits is increased in prio_tree_expand, we shuffle the tree 80 to make sure that the first prio_tree_root->index_bits levels of the tree 81 is indexed properly using heap and radix indices.
	www.mjmwired.net /kernel/Documentation/prio_tree.txt (660 words)

	Integer (Java 2 Platform SE v1.4.2)
		Parses the string argument as a signed integer in the radix specified by the second argument.
		The argument is converted to signed decimal representation and returned as a string, exactly as if the argument and radix 10 were given as arguments to the
		The first argument is interpreted as representing a signed integer in the radix specified by the second argument, exactly as if the arguments were given to the
	java.sun.com /j2se/1.4.2/docs/api/java/lang/Integer.html (1678 words)

	[No title]
		Two radix constants are * involved: One for the bitmaps contained in the leaf nodes (typically * 32), and one for the meta nodes (typically 16).
		The * radix tree should be able to operate well no matter how much * fragmentation there is and no matter how large a bitmap is used.
		* / / * blist_leaf_alloc() - allocate at a leaf in the radix tree (a bitmap).
	web.mit.edu /~netbsd/src/sys/kern/subr_blist.c (2077 words)

	[No title]
		To maintain a search binary tree, it is necessary to store pointers to the left and right sons, and (if we are planning to dynamically reconstruct tree) a pointer to the parent node.
		Each tree covers blocks of N characters, and these blocks overlap so that the characters in any window of size N are in no more than three trees.
		Another reason, is that the insertion of a character in the radix 2 tree may produce up to 8 new nodes, and if we present each node by pair of pointers, this will consume 2*8=16 words of memory, which is quite inefficient.
	www.ee.uwa.edu.au /~roberto/teach/itc314/resources/lzrw1.txt (4047 words)

	[No title] (Site not responding. Last check: )
		py-radix is an implementation of a radix tree data structure for the storage and retrieval of IPv4 and IPv6 network prefixes.
		The radix tree is the data structure most commonly used for routing table lookups.
		The underlying radix tree implementation is taken (and modified) from MRTd and is subject to a 4-term BSD license.
	www2.mindrot.org /files/py-radix/README (288 words)

	Short (Java 2 Platform SE v1.4.2)
		The characters in the string must all be digits, of the specified radix (as determined by whether
		Any character of the string is not a digit of the specified radix, except that the first character may be a minus sign
		in the radix specified by the second argument, exactly as if the argument were given to the
	java.sun.com /j2se/1.4.2/docs/api/java/lang/Short.html (602 words)

	DragonFly kernel List (threaded) for 2005-12
		At the moment I am leaning towards a radix tree because the vast majority of operations will be both non-contended and tend to operate on power-of-2 boundaries.
		Even entities such as inode and bitmap blocks (~6144 byte buffers) would be fairly optimal in a radix tree, the entity would simply have two references from the tree instead of one.
		The problem only occurs when there is a conflict at the boundary because otherwise the storage of the node in the radix tree would simply be in the 'smallest container that fits the whole entity'.
	leaf.dragonflybsd.org /mailarchive/kernel/2005-12/msg00050.html (1009 words)

	Routes storage mechanism (Site not responding. Last check: )
		The Gated route database maintains a single radix tree for all the routes in the database (actually, one per address family).
		The internal nodes of this tree are radix_nodes, and each internal node points to a rt_head structure.
		The routing database in gated is a radix tree, each internal node of which contains a pointer to an rt_head structure.
	www.unix.org.ua /gated/node59.html (2928 words)

	Primer for Radix tree, Help.com (Site not responding. Last check: )
		A radix tree, Patricia trie/tree, or crit bit tree is a specialized set data structure based on the trie that is used to store a set of strings.
		These can be strings of characters, bit strings such as integers or IP addresses, or generally arbitrary sequences of objects in lexicographical order.
		Sometimes the names radix tree and crit bit tree are only applied to trees storing integers and Patricia trie is retained for more general inputs, but the structure works the same way in all cases.
	www.help.com /wiki/Radix_tree (154 words)

	Chapter 4. Networking
		As hinted by the name, the internal structure is a radix tree.
		A radix tree is accessed mostly through the member functions in struct radix_node_head (but there are some exceptions).
		Additionally, the radix tree expects to find the length of the structure underlying the void * at the first byte of the provided argument.
	netbsd.org /Documentation/internals/en/chap-networking-core.html (2819 words)

	ONLamp.com -- Running Zebra on a Unix Machine: An Alternative to a Real Router?
		Since an IP address has 32 bits, the radix tree has a depth of 32 levels, and looking up a route requires a maximum of 32 steps, assuming the right route is present.
		Not all that differently: the 1990 4.3BSD-Reno interim release introduced a radix tree as the data structure for the kernel routing table.
		This is because the radix tree holds the full routing table, so there is no need to rebuild it during process switching.
	www.onlamp.com /pub/a/onlamp/2002/11/07/zebra.html?page=2 (1137 words)

	TERoutingTable
		Performs a pre-order traversal of this radix tree, calculating an estimate of the number of bytes that would be produced by the conversion performed in
		Performs a pre-order traversal of this radix tree and returns a string containing each IP address found along the way.
		Performs a pre-order traversal of this radix tree, converting each node (forwarding table entry) into a series of bytes and inserting them into a given byte array.
	snad.ncsl.nist.gov /glass/doc/api_1.0/SSF/Net/TERoutingTable.html (2120 words)

	Gmane -- Mail To News And Back Again
		Make radix tree lookups safe to be performed without locks.
		Readers are protected against new node insertion by using memory barriers to ensure the node itself will be properly written before it is visible in the radix tree.
		This height does not change after insertion -- when the radix tree is extended, higher nodes are only inserted in the top.
	article.gmane.org /gmane.linux.kernel/355023 (308 words)

	[No title]
		In our assignment 7 situation we are not dealing with digit codes but letter codes and we only have to handle them one at at time such that we map 'a' to 0 on to 'z' as 25.
		I had used a similar method in the extended solution to assignment 5 that is in http://www.psc.edu/~awetzel/asn05soln.c In that case the global variable level was initialized to 0 and then increased it by 1 on every entry to tree_stats() and decereased by 1 on every return.
		In that case it was use just to measure the tree depth and it was natural to think of the first level as level 1.
	www.psc.edu /~awetzel/ds_msg10 (1360 words)

	[No title] (Site not responding. Last check: )
		A radix tree has been chosen to replace the hash because of a neat alignment of XFS inode structures and the kernel radix tree fanout.
		A single radix tree with a read/write lock does not provide enough parallelism to prevent performance regressions on multi-processor machines, so we hash the inode clusters into different radix trees each with their own read/write lock.
		The default is to create (2ncpus)-1 radix* trees up to a maximum of 15.
	oss.sgi.com /cgi-bin/extract-mesg.cgi?a=xfs&m=2006-10&i=20061003060845.GW3024@melbourne.sgi.com (870 words)

	Routes storage mechanism
		The Gated route database maintains a single radix tree for all the routes in the database (actually, one per address family).
		The internal nodes of this tree are radix_nodes, and each internal node points to a rt_head structure.
		The routing database in gated is a radix tree, each internal node of which contains a pointer to an rt_head structure.
	www.pcez.com /~gated/node59.html (2928 words)

	Definition of radix
		5: 100 is the integer to the left of the radix point and 5 is the fractional part to the right.
		To the right of the radix point is 1 which is the binary representation of...
		1: A radix tree is a [[binary search tree]] that is used to...
	www.wordiq.com /search/radix.html (815 words)

	CompressedCaching - linux-mm.org Wiki
		All swap cache pages are part of a single swapper_space – a single radix tree maintains all pages in the swap cache.swp_entry_t is used as a key to locate the corresponding pages in memory.
		The swapper_space radix tree can then be used for ccache too and no separate data structure will be required to save location information of compressed page in ccache structure (i.e.
		The entry in page cache radix tree is now made to point to chunk_head allocated for this compressed page.
	linux-mm.org /CompressedCaching (1952 words)

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