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author | Linus Torvalds <torvalds@linux-foundation.org> | 2024-09-18 06:39:03 +0200 |
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committer | Linus Torvalds <torvalds@linux-foundation.org> | 2024-09-18 06:39:03 +0200 |
commit | 78567e2bc723b444228644d2e34ae5255d4ab8a0 (patch) | |
tree | 3f07fbf68ae127d9c97531a5a80f4eac74acef07 /Documentation/core-api | |
parent | Merge tag 'sound-6.12-rc1' of git://git.kernel.org/pub/scm/linux/kernel/git/t... (diff) | |
parent | cgroup: Do not report unavailable v1 controllers in /proc/cgroups (diff) | |
download | linux-78567e2bc723b444228644d2e34ae5255d4ab8a0.tar.xz linux-78567e2bc723b444228644d2e34ae5255d4ab8a0.zip |
Merge tag 'cgroup-for-6.12' of git://git.kernel.org/pub/scm/linux/kernel/git/tj/cgroup
Pull cgroup updates from Tejun Heo:
- cpuset isolation improvements
- cpuset cgroup1 support is split into its own file behind the new
config option CONFIG_CPUSET_V1. This makes it the second controller
which makes cgroup1 support optional after memcg
- Handling of unavailable v1 controller handling improved during
cgroup1 mount operations
- union_find applied to cpuset. It makes code simpler and more
efficient
- Reduce spurious events in pids.events
- Cleanups and other misc changes
- Contains a merge of cgroup/for-6.11-fixes to receive cpuset fixes
that further changes build upon
* tag 'cgroup-for-6.12' of git://git.kernel.org/pub/scm/linux/kernel/git/tj/cgroup: (34 commits)
cgroup: Do not report unavailable v1 controllers in /proc/cgroups
cgroup: Disallow mounting v1 hierarchies without controller implementation
cgroup/cpuset: Expose cpuset filesystem with cpuset v1 only
cgroup/cpuset: Move cpu.h include to cpuset-internal.h
cgroup/cpuset: add sefltest for cpuset v1
cgroup/cpuset: guard cpuset-v1 code under CONFIG_CPUSETS_V1
cgroup/cpuset: rename functions shared between v1 and v2
cgroup/cpuset: move v1 interfaces to cpuset-v1.c
cgroup/cpuset: move validate_change_legacy to cpuset-v1.c
cgroup/cpuset: move legacy hotplug update to cpuset-v1.c
cgroup/cpuset: add callback_lock helper
cgroup/cpuset: move memory_spread to cpuset-v1.c
cgroup/cpuset: move relax_domain_level to cpuset-v1.c
cgroup/cpuset: move memory_pressure to cpuset-v1.c
cgroup/cpuset: move common code to cpuset-internal.h
cgroup/cpuset: introduce cpuset-v1.c
selftest/cgroup: Make test_cpuset_prs.sh deal with pre-isolated CPUs
cgroup/cpuset: Account for boot time isolated CPUs
cgroup/cpuset: remove use_parent_ecpus of cpuset
cgroup/cpuset: remove fetch_xcpus
...
Diffstat (limited to 'Documentation/core-api')
-rw-r--r-- | Documentation/core-api/index.rst | 1 | ||||
-rw-r--r-- | Documentation/core-api/union_find.rst | 106 |
2 files changed, 107 insertions, 0 deletions
diff --git a/Documentation/core-api/index.rst b/Documentation/core-api/index.rst index f147854700e4..e18a2ffe0787 100644 --- a/Documentation/core-api/index.rst +++ b/Documentation/core-api/index.rst @@ -49,6 +49,7 @@ Library functionality that is used throughout the kernel. wrappers/atomic_t wrappers/atomic_bitops floating-point + union_find Low level entry and exit ======================== diff --git a/Documentation/core-api/union_find.rst b/Documentation/core-api/union_find.rst new file mode 100644 index 000000000000..6df8b94fdb5a --- /dev/null +++ b/Documentation/core-api/union_find.rst @@ -0,0 +1,106 @@ +.. SPDX-License-Identifier: GPL-2.0 + +==================== +Union-Find in Linux +==================== + + +:Date: June 21, 2024 +:Author: Xavier <xavier_qy@163.com> + +What is union-find, and what is it used for? +------------------------------------------------ + +Union-find is a data structure used to handle the merging and querying +of disjoint sets. The primary operations supported by union-find are: + + Initialization: Resetting each element as an individual set, with + each set's initial parent node pointing to itself. + + Find: Determine which set a particular element belongs to, usually by + returning a “representative element” of that set. This operation + is used to check if two elements are in the same set. + + Union: Merge two sets into one. + +As a data structure used to maintain sets (groups), union-find is commonly +utilized to solve problems related to offline queries, dynamic connectivity, +and graph theory. It is also a key component in Kruskal's algorithm for +computing the minimum spanning tree, which is crucial in scenarios like +network routing. Consequently, union-find is widely referenced. Additionally, +union-find has applications in symbolic computation, register allocation, +and more. + +Space Complexity: O(n), where n is the number of nodes. + +Time Complexity: Using path compression can reduce the time complexity of +the find operation, and using union by rank can reduce the time complexity +of the union operation. These optimizations reduce the average time +complexity of each find and union operation to O(α(n)), where α(n) is the +inverse Ackermann function. This can be roughly considered a constant time +complexity for practical purposes. + +This document covers use of the Linux union-find implementation. For more +information on the nature and implementation of union-find, see: + + Wikipedia entry on union-find + https://en.wikipedia.org/wiki/Disjoint-set_data_structure + +Linux implementation of union-find +----------------------------------- + +Linux's union-find implementation resides in the file "lib/union_find.c". +To use it, "#include <linux/union_find.h>". + +The union-find data structure is defined as follows:: + + struct uf_node { + struct uf_node *parent; + unsigned int rank; + }; + +In this structure, parent points to the parent node of the current node. +The rank field represents the height of the current tree. During a union +operation, the tree with the smaller rank is attached under the tree with the +larger rank to maintain balance. + +Initializing union-find +----------------------- + +You can complete the initialization using either static or initialization +interface. Initialize the parent pointer to point to itself and set the rank +to 0. +Example:: + + struct uf_node my_node = UF_INIT_NODE(my_node); + +or + + uf_node_init(&my_node); + +Find the Root Node of union-find +-------------------------------- + +This operation is mainly used to determine whether two nodes belong to the same +set in the union-find. If they have the same root, they are in the same set. +During the find operation, path compression is performed to improve the +efficiency of subsequent find operations. +Example:: + + int connected; + struct uf_node *root1 = uf_find(&node_1); + struct uf_node *root2 = uf_find(&node_2); + if (root1 == root2) + connected = 1; + else + connected = 0; + +Union Two Sets in union-find +---------------------------- + +To union two sets in the union-find, you first find their respective root nodes +and then link the smaller node to the larger node based on the rank of the root +nodes. +Example:: + + uf_union(&node_1, &node_2); |