• Corpus ID: 238856851

Improved Lower Bounds for Strongly Separable Matrices and Related Combinatorial Structures

@inproceedings{Qian2021ImprovedLB,
  title={Improved Lower Bounds for Strongly Separable Matrices and Related Combinatorial Structures},
  author={Bingchen Qian and Xin Wang and Gennian Ge},
  year={2021}
}
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to t positive elements among n samples with as few tests as possible. Disjunct matrices and separable matrices are two classical combinatorial structures while one provides a more efficient decoding algorithm and the other needs fewer tests, i.e., larger rate. Recently, a notion of strongly separable matrix has been introduced, which has the same identifying ability as a… 

References

SHOWING 1-10 OF 21 REFERENCES
2-Cancellative Hypergraphs and Codes
  • Z. Füredi
  • Computer Science, Mathematics
    Combinatorics, Probability and Computing
  • 2012
TLDR
Using an algebraic construction, the previous upper bounds are improved and it is shown that c2(n, 2k) = Θ(nk) for each k when n → ∞.
Families of Finite Sets in Which No Set Is Covered by the Union of Two Others
TLDR
It is proven that f 2 t − 1 (n) ⩽ f 2t (n + 1)⩽ ( t n ) ( t 2t−1 ) with equalities holding iff there exists a Steiner-system S ( t, 2 t−1, n ).
A Better Bound for Locally Thin Set Families
A family of subsets of an n-set is 4-locally thin if for every quadruple of its members the ground set has at least one element contained in exactly 1 of them. We show that such a family has at most
On Cancellative Set Families
TLDR
A new upper bound on the size of 2-cancellative families is provided, improving the previous bound of 20.458n to 20.42n.
Self-Similarity Bounds for Locally Thin Set Families
TLDR
This paper derives a new exponential upper bound for the maximum size of set families of subsets of an n-set if, for every k-tuple of its members, the ground set has at least one element contained in exactly one of them.
New rate pairs in the zero-error capacity region of the binary multiplying channel without feedback
  • L. Tolhuizen
  • Mathematics, Computer Science
    IEEE Trans. Inf. Theory
  • 2000
TLDR
This work constructs uniquely decodable (UD) code pairs for the binary multiplying channel without feedback, using pairs of binary codes and obtains an asymptotically optimal construction for the combinatorial concept of cancellative families of sets.
A New Construction for Cancellative Families of Sets
  • J. Shearer
  • Mathematics, Computer Science
    Electron. J. Comb.
  • 1996
TLDR
This work shows how to construct cancellative families of sets with c 2.54797n elements and improves the previous best bound and falsifies conjectures of Erdos and Katona and Bollobas.
Union-free Hypergraphs and Probability Theory
TLDR
It is proved that 2(n-log3)/3 - 2 ≤ F(n) ≤ 2(3n+2)/4, which is the maximum number of distinct subsets of an n-element set such that there are no four distinct subs sets.
Combinatorial Group Testing and Its Applications
Group testing was first proposed for blood tests, but soon found its way to many industrial applications. Combinatorial group testing studies the combinatorial aspect of the problem and is
String Quartets in Binary
TLDR
It is shown that there is an absolute constant c < 1/2 such that M(n, C) [les ] 2cn for all sufficiently large n.
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