Optimization over Degree Sequences

@article{Deza2018OptimizationOD,
  title={Optimization over Degree Sequences},
  author={Antoine Deza and Asaf Levin and Syed Mohammad Meesum and Shmuel Onn},
  journal={SIAM J. Discret. Math.},
  year={2018},
  volume={32},
  pages={2067-2079}
}
We introduce and study the problem of optimizing arbitrary functions over degree sequences of hypergraphs and multihypergraphs. We show that over multihypergraphs the problem can be solved in polynomial time. For hypergraphs, we show that deciding if a given sequence is the degree sequence of a 3-hypergraph is NP-complete, thereby solving a 30 year long open problem. This implies that optimization over hypergraphs is hard already for simple concave functions. In contrast, we show that for… 
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19 Citations
Highly Influential Citations
3
Background Citations
9
Methods Citations
3
Results Citations
1

19 Citations

Optimization over Degree Sequences of Graphs
On Degree Sequence Optimization
  • S. Onn
  • Mathematics, Computer Science
    Oper. Res. Lett.
  • 2020
Reconstruction of hypergraphs from line graphs and degree sequences
In this paper we consider the problem to reconstruct a k-uniform hypergraph from its line graph. In general this problem is hard. We solve this problem when the number of hyperedges containing any…
On the Degree Sequence of 3-Uniform Hypergraph: A New Sufficient Condition
The study of the degree sequences of h-uniform hypergraphs, say h-sequences, was a longstanding open problem in the case of \(h>2\), until very recently where its decision version was proved to be…
Construction of Simplicial Complexes with Prescribed Degree-Size Sequences
TLDR
It is found that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes, which unveils a fundamental constraint on the degree-size sequences.
On null 3-hypergraphs
Separable and Equitable Hypergraphs
A k -hypergraph is separable if its vertices admit a certain labeling, and is equitable if the edges of the complete k -hypergraph admit a certain labeling. We show that these classes of hypergraphs…
On Line Sum Optimization
  • S. Onn
  • Mathematics
    Linear Algebra and its Applications
  • 2021
On the Computational Complexity of Finding Bipartite Graphs with a Small Number of Short Cycles and Large Girth
TLDR
It is proved that for a given set of integers $\alpha, \beta$, and $\gamma$, and degree sequences $\pi$ and $\pi$’, the problem of determining whether there exists a simple bipartite graph with degree sequences $(\pi,\ \pi')$ that has at most $\alpha$ ($\beta$ and $\Gamma$) cycles of length four is NP-complete.
On the Hypercube Subset Partitioning Varieties
TLDR
The NP-hardness of the QDP problem is proved and it is shown that QDP are in a correspondence to the upper homogeneous area elements of the n-cube and to the monotone Boolean functions.
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