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The multiple subset sum problem is an optimization problem in computer science and operations research. It is a generalization of the subset sum problem . The input to the problem is a multiset S {\displaystyle S} of n integers and a positive integer m representing the number of subsets.
Let C i (for i between 1 and k) be the sum of subset i in a given partition. Instead of minimizing the objective function max(C i), one can minimize the objective function max(f(C i)), where f is any fixed function. Similarly, one can minimize the objective function sum(f(C i)), or maximize min(f(C i)), or maximize sum(f(C i)).
The variant in which all inputs are positive, and the target sum is exactly half the sum of all inputs, i.e., = (+ +). This special case of SSP is known as the partition problem . SSP can also be regarded as an optimization problem : find a subset whose sum is at most T , and subject to that, as close as possible to T .
Balanced number partitioning is a variant of multiway number partitioning in which there are constraints on the number of items allocated to each set. The input to the problem is a set of n items of different sizes, and two integers m, k.
In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S). In multiway number partitioning , there is an integer parameter k , and the goal is to decide whether S can be partitioned into k subsets of equal sum ...
The required output is a partition of S into k subsets, such that the sums in the subsets are as nearly equal as possible. Greedy algorithms process the numbers sequentially, and insert the next number into a bin in which the sum of numbers is currently smallest.
Partitioning is commonly implemented alongside replication, storing partition copies across multiple nodes. Each record belongs to one partition but may exist on multiple nodes for fault tolerance. In leader-follower replication systems, nodes can simultaneously serve as leaders for some partitions and followers for others. [1]
The snowflake schema is in the same family as the star schema logical model. In fact, the star schema is considered a special case of the snowflake schema. The snowflake schema provides some advantages over the star schema in certain situations, including: Some OLAP multidimensional database modeling tools are optimized for snowflake schemas. [3]