Everything about Multiple subset sum
Mathematical optimization problem
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 of n integers and a positive integer m representing the number of subsets. The goal is to construct, from the input integers, some m subsets. The problem has several variants:Max-sum MSSP: for each subset j in 1,...,m, there is a capacity Cj. The goal is to make the sum of all subsets as large as possible, such that the sum in each subset j is at most Cj. Max-min MSSP : again each subset has a capacity, but now the goal is to make the smallest subset sum as large as possible. Fair SSP: the subsets have no fixed capacities, but each subset belongs to a different person. The utility of each person is the sum of items in his/her subsets. The goal is to construct subsets that satisfy a given criterion of fairness, such as max-min item allocation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Multiple subset sumA 5-minute orientation
- Pick up a classic book: The little SAS bookThe most-reprinted book on the subject
- Read the landmark paper: The Multiple Subset Sum ProblemCited 79 times
- Go sideways: Knapsack problemA closely related topic
- Go sideways: List of knapsack problemsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
📚 Books worth reading
The little SAS bookLora D. Delwiche, Susan J. Slaughter · 1995
Introduction to Probability and StatisticsJ. Susan Milton, Jesse C. Arnold · 1990
Introduction to Multiple Time Series AnalysisHelmut Lütkepohl, Helmut Lutkepohl · 1991
Abstract algebraDavid S. Dummit · 1991
Computer algorithmsEllis Horowitz · 1997
Fundamentals of computer algorithmsEllis Horowitz · 1978
2000 Solved Problems in Discrete MathematicsSeymour Lipschutz · 1991
Introduction to combinatoricsMartin J. Erickson · 1996
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Knapsack problem The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items…
- List of knapsack problems The knapsack problem is one of the most studied problems in combinatorial optimization, with many real-life applications. For this reason, many special…
- Fully polynomial-time approximation scheme A fully polynomial-time approximation scheme (FPTAS) is an algorithm for finding approximate solutions to function problems, especially optimization problems…
- APX In computational complexity theory, the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time…
- Subset sum problem The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S of integers and a target-sum…
- Maximin share Maximin share (MMS) is a criterion of fair item allocation. Given a set of items with different values, the 1-out-of-n maximin-share is the maximum value…
- Matroid-constrained number partitioning Matroid-constrained number partitioning is a variant of the multiway number partitioning problem, in which the subsets in the partition should be independent…
- Quadratic knapsack problem The quadratic knapsack problem (QKP), first introduced in 19th century, is an extension of knapsack problem that allows for quadratic terms in the objective…