# Questions tagged [decomposition]

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### Global optimization of state assignments in a directed graph with a tree-based distance cost

I am exploring a general optimization framework to solve problems characterized by the following structure. Any literature references, search terms, or algorithmic strategies would be greatly ...
• 151
1 vote
153 views

### Learning eigenvalue decomposition

How would you build a fully connected neural network that learns eigenvalue decomposition efficiently? I wanted to build NNs that can predict certain properties about matrices which are NP-hard to ...
• 113
1 vote
57 views

### Relationships between path width and clique size of interval graphs

I faced the following claim on wikiepdia about interval graphs (https://en.wikipedia.org/wiki/Interval_graph): The pathwidth of an interval graph is one less than the size of its maximum clique. I ...
391 views

### Converting a Directed Acyclic Graph to a Directed Tree

I'm wondering if anyone can help me with this. Say I have a DAG, I understand that it has no directed cycles, but it can have loops ( "diamonds" ). My question is, is there a known way to ...
105 views

### Integer decomposition algorithm

Suppose I have a 32-bit integer $x$, I want to find $\{ x_i \}_{i \in 1\dots\ell}$ such that $x = e + \sum_{i=1}^\ell x_i \cdot 2^{32 - B\cdot i}$ where the error $e$ is as small as possible. The ...
• 107
183 views

### Is this decomposition in 3NF?

I have the following question: Consider relation R(A, B, C, D, E, F, H) with the following functional dependencies: A --> D, AE --> H, DF --> BC, E --> C, H --> E Consider three ...
145 views

• 273
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### Fine-Grain parallel algorithm for LU-decomposition

How would you understand this pseudocode of parallel algorithm for LU-decomposition ? I'm confused mostly with the min(i; j) - 1, because I have no idea, what the ...
• 242
1 vote
2k views

### Parallel algorithm for LU-decomposition

I need to implement LU-decomposition in Kaira. In Kaira the programmer writes the "parallel part" as the diagram similar to Petri Nets. So, could you, please, recommend me some parallel algorithms ...
• 242
1k views

### BCNF Decomposition: Confusion regarding given answer

I encountered the following question: Given a relation R(A, B, C, D) with the following functional dependencies: A -> B, C -> D, B -> C. The BCNF Decomposition of R is: A) {(A,B), (C,D), (B,C)} B) {...