Asymptotically Optimal Covering Designs

نویسندگان

  • Daniel M. Gordon
  • Oren Patashnik
  • Greg Kuperberg
  • Joel H. Spencer
چکیده

A (v, k, t) covering design, or covering, is a family of k-subsets, called blocks, chosen from a v-set, such that each t-subset is contained in at least one of the blocks. The number of blocks is the covering’s size, and the minimum size of such a covering is denoted by C(v, k, t). It is easy to see that a covering must contain at least (v t )

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Efficient Covering Designs of the Complete Graph

Let H be a graph. We show that there exists n0 = n0(H) such that for every n ≥ n0, there is a covering of the edges of Kn with copies of H where every edge is covered at most twice and any two copies intersect in at most one edge. Furthermore, the covering we obtain is asymptotically optimal.

متن کامل

Eecient Covering Designs of the Complete Graph

Let H be a graph. We show that there exists n 0 = n 0 (H) such that for every n n 0 , there is a covering of the edges of K n with copies of H where every edge is covered at most twice and any two copies intersect in at most one edge. Furthermore, the covering we obtain is asymptotically optimal.

متن کامل

Packing and Covering Properties of CDCs and Subspace Codes

Codes in the projective space over a finite field, referred to as subspace codes, and in particular codes in the Grassmannian, referred to as constant-dimension codes (CDCs), have been proposed for error control in random network coding. In this paper, we first study the covering properties of CDCs. We determine some fundamental geometric properties of the Grassmannian. Using these properties, ...

متن کامل

Two-stage designs applying methods differing in costs

MOTIVATION Two-stage pilot and integrated designs are powerful tools for investigating large numbers of hypotheses. Asymptotically, optimal two-stage designs controlling the familywise error or false discovery rate are considered when costs and effect sizes per measurement differ between stages and total costs are constrained. RESULTS Depending on the cost and effect size ratios between the m...

متن کامل

Quantization of Discrete Probability Distributions

We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit simplex. Such setting yields precise asymptotic characterization in the high-rate regime. Our main contribution is a simple and asymptotically optimal algorithm fo...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • J. Comb. Theory, Ser. A

دوره 75  شماره 

صفحات  -

تاریخ انتشار 1996