Football Pools--A Game for Mathematicians

Hamalainen, H.O.; Honkala, Iiro; Litsyn, Simon; Östergård, Patric R. J.

doi:10.2307/2974552

Cited by 22 publications

(11 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Solving the football pools problem completely requires the determination of a ternary code of length N and covering radius at least N 0 K (see [3] and the references therein) containing the minimum possible number of codewords. A ternary code of length N has covering radius R if every ternary N -vector is at most at Hamming distance R from some codeword.…”

Section: An Application To Football Poolsmentioning

confidence: 99%

Comments on "An inequality on guessing and its application to sequential decoding"

Boztaş

1997

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

Section: An Application To Football Poolsmentioning

confidence: 99%

Comments on "An inequality on guessing and its application to sequential decoding"

Boztaş

1997

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…be the density of an (n, M) q R covering code C. In general, δ(C, R) ≥ 1, and equality holds if and only if C is a perfect code. 3,6,19,20]).…”

Section: Multiple Coverings and (ρ µ)-Saturating Setsmentioning

confidence: 99%

Further results on multiple coverings of the farthest-off points

Bartoli¹,

Davydov²,

Giulietti³

et al. 2016

AMC

View full text Add to dashboard Cite

Multiple coverings of the farthest-off points ((R, µ)-MCF codes) and the corresponding (ρ, µ)-saturating sets in projective spaces P G(N, q) are considered. We propose and develop some methods which allow us to obtain new small (1, µ)-saturating sets and short (2, µ)-MCF codes with µ-density either equal to 1 (optimal saturating sets and almost perfect MCF-codes) or close to 1 (roughly 1 + 1/cq, c ≥ 1). In particular, we provide new algebraic constructions and some bounds. Also, we classify minimal and optimal (1, µ)-saturating sets in P G(2, q), q small.

show abstract

“…The football problem is a popular problem from coding theory [16], due to its application to gambling on football (soccer) games. A gambler wishes to bet on n football games.…”

Section: Case Study: the Football Pool Problemmentioning

confidence: 99%

Using Symmetry to Optimize Over the Sherali-Adams Relaxation

Ostrowski

2012

Lecture Notes in Computer Science

View full text Add to dashboard Cite

In this paper we examine the impact of using the Sherali-Adams procedure on highly symmetric integer programming problems. Linear relaxations of the extended formulations generated by Sherali-Adams can be very large, containing O(n d) many variables for the level-d closure. When large amounts of symmetry are present in the problem instance however, the symmetry can be used to generate a much smaller linear program that has an identical objective value. We demonstrate this by computing the bound associated with the level 1, 2, and 3 relaxations of several highly symmetric binary integer programming problems. We also present a class of constraints, called counting constraints, that further improves the bound, and in some cases provides a tight formulation. A major advantage of the Sherali-Adams formulation over the traditional formulation is that symmetry-breaking constraints can be more efficiently implemented. We show that using the Sherali-Adams formulation in conjunction with the symmetry breaking tool isomorphism pruning can lead to the pruning of more nodes early on in the branch-and-bound process.

show abstract

Football Pools--A Game for Mathematicians

Cited by 22 publications

References 0 publications

Comments on "An inequality on guessing and its application to sequential decoding"

Comments on "An inequality on guessing and its application to sequential decoding"

Further results on multiple coverings of the farthest-off points

Using Symmetry to Optimize Over the Sherali-Adams Relaxation

Contact Info

Product

Resources

About