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Everything about Set packing
Problem in computer science
Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose one has a finite set S and a list of subsets of S. Then, the set packing problem asks if some k subsets in the list are pairwise disjoint. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Set packingA 5-minute orientation
- Skim a recent paper: Learning generalized strong branching for set covering, set packing, and 0–1 knapsack problemsInfluential work since 2022
- Pick up a classic book: The Beech-Nut bookThe most-reprinted book on the subject
- Read the landmark paper: On the facial structure of set packing polyhedraCited 452 times
- Go sideways: 3-dimensional matchingA closely related topic
- Go sideways: Independent set (graph theory)A closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
On the facial structure of set packing polyhedra
Efficient bounds for the stable set, vertex cover and set packing problems
On the complexity of approximating k-set packing
Greedy Local Improvement and Weighted Set Packing Approximation
On Local Search for Weighted k-Set Packing
A Set-Covering-Based Heuristic Approach for Bin-Packing Problems
Level-set-based partitioning and packing optimization of a printable model
GRASP for set packing problems
🆕 Influential since 2022
Learning generalized strong branching for set covering, set packing, and 0–1 knapsack problems
Understanding the structure and dynamics of local powder packing density variations in metal additive manufacturing using set Voronoi analysis
CMSA based on set covering models for packing and routing problems
The limits of local search for weighted k-set packing
On the Hausdorff dimension of the residual set of a packing by smooth curves
📚 Books worth reading
- 📕The Beech-Nut bookIda Cogswell Bailey Allen, Beech-Nut Packing Co · 1924
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- 3-dimensional matching In the mathematical discipline of graph theory, a 3-dimensional matching is a generalization of bipartite matching (also known as 2-dimensional matching)…
- Independent set (graph theory) In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a…
- Domatic number In graph theory, a domatic partition of a graph G=(V,E) is a partition of V into disjoint sets V1, V2,...,VK such that each Vi is a dominating set for…
- Set cover problem The set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory. Given a set of elements {1…
- Vertex cover In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph.…
- Matroid parity problem In combinatorial optimization, the matroid parity problem is a problem of finding the largest independent set of paired elements in a matroid, a structure…
- Feedback arc set In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at…
- Clique cover In graph theory, a clique cover or partition into cliques of a given undirected graph is a collection of cliques that cover the whole graph. Generally…