Local depth and global depth in extendible hashing. Every bucket has a local depth leqd.

Local depth and global depth in extendible hashing. Before insert, local depth of bucket = global depth. The global depth may also need to increase if all bits of the hash value are used. Question 2: Extendible Hashing The final global depth is 2, with the directory pointing to buckets that have local Jun 10, 2025 · Local depth in accordance with the global depth is used to decide the action that to be performed in case an overflow occurs. The difference between local depth and global depth affects overflow handling. 3 illustrates the extendible hashing after inserting 17 and 13 into Fig. Insert causes local depth to become > global depth; directory is doubled by copying it over and ‘fixing’ pointer to split image page. This implementation uses the least-significant bits. ) Before insert, local depth of bucket = global depth. Jan 27, 2024 · The image above has two directory slots pointing to one bucket because the global depth is 2 and the local depth of the bucket is 1. Use the following information to answer questions . Jul 12, 2025 · Local depth in accordance with the global depth is used to decide the action that to be performed in case an overflow occurs. 3. Global depth of directory: Max # of bits needed to tell which bucket an entry belongs to. The local depth of the overflowing bucket is increased, and a new bucket is created. What Does Growth And Shrinkage Look Like When an extendible Extendible hashing steps Hash the data Match “global depth” number lower significant bits of the hashed data to the corresponding directory id Go to bucket pointed by directory and insert if there is no overflow. Overflow Handling is split into two. Global depth of a directory - max # of bits needed to tell which bucket an entry belongs to. Nov 4, 2021 · Extendible Hash Table 属于动态哈希的一种，网上有很多关于它的介绍，但是真的在实现它的时候，或多或少有着很多问题。网上很多教程光讲怎么扩容，不讲收缩，而且网上很多都是概念性的东西，不讲代码实操。因 CMU 15-445 的课程需要，自己捣鼓了一下算法流程，这里分享一下。 在看之前请自行了解 – The local depth represents the number of bits used for hashing in a bucket. { When does bucket split cause directory doubling? Before inserting, local depth of bucket = global depth Inserting causes local depth to become > global depth { Directory is doubled by copying it over and adjusting pointer to split image page (use of least significant bits enables efficient doubling via copying of directory!) Before insert, local depth of bucket = global depth. Refer Fig. If the local depth exceeds the global depth, the global depth is also increased, doubling the directory size. Directories store bucket addresses in pointers. Jan 5, 2025 · The bucket is split: The local depth of the bucket increases by 1. Local Depth is always <= Global Depth If d' for the overflowed bucket is less than d, the global depth, then a new bucket is allocated. 2 Jul 12, 2025 · Local depth in accordance with the global depth is used to decide the action that to be performed in case an overflow occurs. a. Examining the initial case of an extendible hash structure, if each directory entry points to one bucket, then the local depth should be equal to the global depth. Complex Implementation Requires careful handling of Jan 26, 2024 · You have some key which you hash with some uniformly distributed hash function and the resulting hash can be represented in 32 bits. The integer value corresponding to the first (high-order) d bits of a hash value is used as an index to the array to determine a directory entry, and the address in that entry determines the bucket 7. Each SwissTable also has a Before insert, local depth of bucket = global depth. Entries in the bucket are redistributed based on their updated hash values. Global Depth = Number of bits in directory id. Mar 8, 2016 · Global depth of directory: Max # of bits needed to tell which bucket an entry belongs to. The size of the directory is 1 « globalDepth i. For simplicity assume the adopted hash function is h (k) = k. Global depth denotes the number of bits used by the hash function, while local depth is associated with buckets. The directory may or may not double, depending on whether the local depth of the overflown bucket was equal to the global If the local depth was equal to global depth, overflown bucket. Question 1: Extendible Hashing The final global depth is 3, with the directory pointing to buckets that have local depths of either 1, 2, or 3 depending on the splits. Directory Doubling 00 01 10 11 2 Why use least significant bits in directory (instead of the most significant ones)? Before insert, local depth of bucket = global depth. – The directory size is doubled when a bucket becomes full. Use the following set of values to construct the hash table and show how values are placed into data-buckets of size 4. The size of each bucket is 2 records. Demonstrate the extendible hashing technique with following assumptions: Local depth=2, Global depth=2, Number of buckets=4, insertion of data records with hash key values: 8, 36, 25, 33, 14, 18, 19, 23, 35, 22, 47, 30, 41, 40, 48, 49, 42, 51, 54, 61, 68, 9, 4, 6, 10,11 and 63. The initial global depth value is 0 and the directory entry points to an empty bucket. Disadvantages of Extendible Hashing Directory Doubling is Expensive When the global depth increases, the entire directory size doubles, which can be expensive in terms of memory and performance. Directories store pointers to buckets, which store hashed keys. Extendible hashing is a dynamic hashing method that uses directories and buckets to hash data. May 17, 2016 · Current global depth is 2 and local depth at B2 is also 2. – Before insert, local depth of bucket = global depth. • Increase local depth of Bucket 0 to 2. Each directory has a dynamically changing id. The values are omitted, and the hash of the keys are shown in the bucket pages instead of the key themselves. Number of Directories = 2^Global Depth. You take the max depth number of most significant bits to find the correct directory from the header and the global depth number of least significant bits to find the correct bucket from the directory. Describe Extendible Hashing and construct a hash table using hash function H (r) Binary equivalent of r, i. The hash function returns this directory id which is used to navigate to the appropriate bucket. Sep 20, 2024 · When a bucket overflows, it must be split. In extendible hashing, a type of directory—an array of 2d bucket addresses—is maintained, where d is called the global depth of the directory. The hash table has the notion of a global depth, it guarantees that each data page we use will have the same depth bits in it. Example Implementation in Python – The extendible hashing algorithm can be implemented in Python. • In extendible hashing, last bits d is called global depth for directory and d is called local depth for data pages or buckets. 2^d entries. However, the bucket numbers will at all times use some smaller number of bits, say i bits, from the beginning or end of this sequence. Global Depth: Number of bits in directory id Local Depth: Number of bits in bucket id. Local depth of a bucket: # of bits used to determine if an entry belongs to this bucket. 2 Bucket C Bucket D (allocate new page, re-distribute). Each bucket has associated with it a local depth denoted d'. Both the new bucket and the overflowed bucket are assigned local depth d'+1. Pointers in directory locations are stored as explained before. (Follow the same order while mapping on to the buckets) (7M) b. After insetion of 20*, the global depth becomes 3 as we consider last three bits and local depth of A and A2 buckets become 3 as we are considering last three bits for placing the data records. Can you identify this hash function? Insert 20 20* LOCAL DEPTH GLOBAL DEPTH 2 2 4*12* 32* 16* Bucket A 什么时候 table (directory) 进行 double？当 d = d' 时，比如左图bucket B，要插入 100，由于bucket已满，发生冲突，按照上面的方式思考，就会想 split，但是我们发现 global depth 才是2，local depth 已经是2，不能进行 split 使 local depth 增一了，所以要将 directory 进行double，global depth增一，如右图所示，采用每个数的 Mar 27, 2012 · Extendible Hashing - Class Example splitting bucket splitting bucket rec 1 d1=0 0 rec 2 1 record 3 = overflow!! record 5 = overflow!! d1 = 1 d1 = 1 d1 = local depth d = global depth rec 1 rec 4 d = 0 d = 1 rec 2 rec 3 NEXT rec 1 rec 4 splitting bucket 00 01 10 record 7 = overflow!! 11 d = 2 d1 = 2 d1 = 2 d1 = 1 rec 2 rec 3 rec 5 rec 6 NEXT The hash function h computes for each key a sequence of k bits for some large k, say 32. 1. It uses a flexible hash function that can dynamically change. A new split image of B2 is created as B2*. The values are 0, 1, 4, 2, 3, 5, 8, 13, 21, 34, 55. Example of Linear Hashing On split, hLevel+1 is used to re-distribute entries. When the hash function is applied to the keys of these records, the values 0, 1, 2 Jan 26, 2024 · You have some key which you hash with some uniformly distributed hash function and the resulting hash can be represented in 32 bits. Local depth in accordance with the global depth is used to decide the action that to be performed in case an overflow occurs. If bucket overflows and local depth = global depth, expand directory, split bucket, and then increment local and global depth number. Local Depth is always less than or equal to the Global Depth. Local depth of a bucket - # of bits used to determine if an entry belongs to this bucket. e. 4. 1110, goes into 3 rdbucket To split an overflown bucket whose local depth is smaller than the global depth, one does not need to double the size of the directory. When does split cause directory doubling? Before insert, local depth of bucket = global depth. Study with Quizlet and memorize flashcards containing terms like Extendible hashing is a dynamic hashing method that, Inserting a new entry to the table can result in four possible actions, Page Split and more. The hash function also uses a bitmask to blend out unnecessary bits. Each directory is given a unique id which may change each time when expansion takes place. If d' for the overflowed bucket is less than d, the global depth, then a new bucket is allocated. Mar 6, 2023 · Extendible Hash Table 最近在学习CMU的15-445 DB课程，在做Project1的Extendible Hash Table的时候，由于是先看了课程，过了一个多星期才做的Lab，对extendible hash table只能说是知道大体的意思，并没有透彻的了解它，尤其是bucket指针和数据重分配这一部分，涉及到比较tricky的位运算，在一知半解的情况下实现它 Extendible HashingBackground最近在学习CMU 2021的15-445课程， 其中lab2便是要实现一个Extendible Hash， 实验过程踩了不少的坑，在这里记录一下。 Extendible Hashing 正如其名， 是一种可扩展哈希表， 可扩展… 10 Example 00 13* 01 10 11 2 2 2 2 2 LOCAL DEPTH GLOBAL DEPTH DIRECTORY Bucket A Bucket B Bucket C Bucket D DATA PAGES 10* 1* 21* 4* 12* 32* 16* 15* 7* 19* 5* Notation: 1* = data entry with hash value 1 To find bucket for record with key k, look at last 2 bits of h(k) E. Extendible Hashing The dynamic hashing technique that uses directories. Every bucket has a local depth leqd. EXTENDIBLEHASHING To search, use the last2 digits of the binary formof the search key value local depth global depth 2 (John, 12, 23218564) 2 Mar 10, 2024 · The following diagram shows an extendible hash table with a header page of max depth 2, directory pages with max depth 2, and bucket pages holding at most two entries. 可扩展hash (Extendible Hashing ) 是一种动态 hash 方法. Local Depth is always <= Global Depth Global depth of directory: Max # of bits needed to tell which bucket an entry belongs to. Directory size doubles (from 2 to 4). So when B2 splits and we start using 3 bits from the hash value, we can’t really do that without doubling the directory size from 4 to 8 and thus incrementing I to 3. Insert causes local depth to become > global depth; directory is doubled by copying it over and `fixing’ pointer to split image page. Consider the following disk request sequence Jun 4, 2025 · The magic of extendible hashing is in the way, the hash table is resized, both at the individual hash table as well as the Directory. Jul 12, 2025 · Local Depth: It is the same as that of Global Depth except for the fact that Local Depth is associated with the buckets and not the directories. So the hash consists only of d bits. For instance, Fig. Suppose extendible hashing is used to organize a file of data records. Your attempt should show local depth, global depth,. Jan 27, 2024 · A header maintains a max depth, a directory maintains a global depth and a bucket maintains a local depth. (Splitting a bucket does not always require doubling; we can tell by comparing global depth with local depth for the split bucket. An example of extendible hashing is shown in Fig. When a bucket overflows, the directory doubles in size and the Apr 18, 2022 · 当插入22的时候，产生overflow，那么此时就扩展directory，以及重新hash，更新global depth和local depth 当再次插入满的时候，继续判断是否local depth 等于 global depth，如果等于，那么还是执行上述操作 Extendible hashing is a type of hash system which treats a hash as a bit string and uses a trie for bucket lookup. g. Question: a) Explain why local depth and global depth are needed in Extendible (or Extendable) Hashing? b) After insertion into an Extendible Hashing-based index that causes the directory size to double, how many buckets have exactly one directory entry pointing to them? Before insert, local depth of bucket = global depth. H (5) = 101. The global depth and all the four local depths are 2. The directory is updated to reflect the new structure, which may involve duplicating entries if the global depth changes. if h(k) = 14 i. A sequence of 11 records are to be inserted into the file. Extendible Hashing The purpose of this project is to grasp the basic concepts of Database Management Systems and the improvement in performance Hash Tables can bring. Since buckets are split round-robin, long overflow chains don’t develop! Doubling of directory in Extendible Hashing is similar; switching of hash functions is implicit in how the # of bits examined is increased. 0 h h 1 (This info is for illustration only!) Feb 13, 2022 · 15-445 (2021) PROJECT #2 - EXTENDIBLE HASH INDEX TASK #1 - PAGE LAYOUTS 先看一下这张图片，留一个对extendible hashing的印象： 左边那个就是directory page，它有一个参数叫做global depth，1<<global depth为directory的大小。 它存储了指向各个bucket page的指针。 Local Depth: 它与 global depth 一个道理，只是 local depth 与 bucket 而不是 directory 相关联。 根据 global depth，使用 local depth 来决定在发生 \color {red} {overflow} 时执行的动作。 Mar 28, 2019 · 这时先将bucket address table扩大一倍，同时global depth加1。 然后重新创建两个新的bucket a, bucket b，local depth在原来local depth基础上加1（由0变为1），再将bucket 1中的 [1, v], [2, v]分配到新的两个bucket中，分配规则如下： • Bucket 0 is split into two: one bucket will store items with hash ending in 0, and the other will store items with hash ending in 1. Thus a directory doubling occurs, which effectively uses one more bit f Jan 1, 2018 · If the local depth was equal to global depth, d bits are not enough to distinguish the search values of the overflown bucket. Thus a directory doubling occurs, which effectively uses one more bit from the hash value. Insertion where d' < d: It is for insertion causing bucket overflow that things get interesting. [1] Because of the hierarchical nature of the system, re-hashing is an incremental operation (done one bucket at a time, as needed). Extendible Hashing is a dynamic hashing method wherein blocks and buckets are used to hash data. – After a bucket split, the local depth is incremented and used for redistributing the entries. Since we are using least significant bits in the directory in our example, global depth = number of least significant bits needed to identify bucket. • Increase global depth to 2 (because the local depth of the bucket exceeds the global depth). Local Depth: It is the same as that of Global Depth except for the fact that Local Depth is associated with the buckets and not the directories. Instead of using the entire hash value of the key at once, it looks at a certain number of bits from the beginning of the hash – let's call this the global depth (d). If necessary, double the directory. It is a flexible method in which the hash function also experiences changes. When does bucket split cause directory doubling? Before insert, local depth of bucket = global depth. Each bucket holds up to 2 employee IDs, distributed based on the first 3 bits of their binary representation. Instead, half of the 2d d0 directory entries will point to the new bucket, and the local depth of both the over-flown bucket and its split image are increased by one. 2 – Copy directory – Change pointer of directory entry m+2b+i Keep track of how many bits actually using – depth of directory: global depth – depth of each bucket: local depth (WHY KEEP?) new 7 • What did we do? Dec 17, 2019 · We can take advantage on a feature of the extendible hashing. Jan 26, 2024 · You have some key which you hash with some uniformly distributed hash function and the resulting hash can be represented in 32 bits. Frequently used terms in Extendible Hashing: 在可扩展哈希中常用术语 Directories: These containers store pointers to buckets. 12. To split an overflown bucket whose local depth is smaller than the global depth, one does not need to double the size of the directory. This however depends entirely on the size of the array, which is defined as 2d, with d being the global depth. Hash the key, take d bits to find the index, follow the hash table entry to the target bucket. High Memory Usage for Directory The directory can become large, especially if many buckets have a low local depth and point to unique entries. 目录: 这个容器存储指向 Jul 15, 2024 · 可扩展Hash 可扩展Hash是结合了Hash算法的一种数据结构组织方法, 这种数据组织方式涉及到Hash函数, 目录映射存储地址, 使用Hash函数的结果作为地址下标的索引, 以及使用桶的方式存储键值对数据. Here there are four directory entries and four buckets. mcsfu ixynjad rzvvso khpkfz syja gxhv hrpmr cpf egz iul