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A common special case called two-way balanced partitioning is when there should be two subsets (m = 2). The two subsets should contain floor(n/2) and ceiling(n/2) items. It is a variant of the partition problem. It is NP-hard to decide whether there exists a partition in which the sums in the two subsets are equal; see [4] problem [SP12]. There ...
In number theory and computer science, the partition problem, or number partitioning, [1] is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S 1 and S 2 such that the sum of the numbers in S 1 equals the sum of the numbers in S 2. Although the partition problem is NP-complete, there is a ...
Otherwise, open a new bin and put the new item in it. The algorithms differ in the criterion by which they choose the open bin for the new item in step 1 (see the linked pages for more information): Next Fit (NF) always keeps a single open bin. When the new item does not fit into it, it closes the current bin and opens a new bin.
A block, a contiguous number of bytes, is the minimum unit of storage that is read from and written to a disk by a disk driver.The earliest disk drives had fixed block sizes (e.g. the IBM 350 disk storage unit (of the late 1950s) block size was 100 six-bit characters) but starting with the 1301 [8] IBM marketed subsystems that featured variable block sizes: a particular track could have blocks ...
[1]: sec.5 The problem is parametrized by a positive integer k, and called k-way number partitioning. [2] The input to the problem is a multiset S of numbers (usually integers), whose sum is k*T. The associated decision problem is to decide whether S can be partitioned into k subsets such that the sum of each subset is exactly T.
The limit on partition size was dictated by the 8-bit signed count of sectors per cluster, which originally had a maximum power-of-two value of 64. With the standard hard disk sector size of 512 bytes, this gives a maximum of 32 KB cluster size, thereby fixing the "definitive" limit for the FAT16 partition size at 2 GB for sector size 512.
2 + 2 2 + 1 + 1 1 + 1 + 1 + 1. The only partition of zero is the empty sum, having no parts. The order-dependent composition 1 + 3 is the same partition as 3 + 1, and the two distinct compositions 1 + 2 + 1 and 1 + 1 + 2 represent the same partition as 2 + 1 + 1. An individual summand in a partition is called a part.
Consider a graph G = (V, E), where V denotes the set of n vertices and E the set of edges. For a (k,v) balanced partition problem, the objective is to partition G into k components of at most size v · (n/k), while minimizing the capacity of the edges between separate components. [1]