Golomb rectangles as folded rulers
نویسنده
چکیده
منابع مشابه
A review of the available construction methods for Golomb rulers
We collect the main construction methods for Golomb rulers available in the literature along with their proofs. In particular, we demonstrate that the Bose-Chowla method yields Golomb rulers that appear as the main diagonal of a special subfamily of Golomb Costas arrays. We also show that Golomb rulers can be composed to yield longer Golomb rulers.
متن کاملOn the Design of Optimum Order 2 Golomb Ruler
A Golomb ruler with M marks can be defined as a set {ai} of integers so that all differences δij = aj − ai, i 6= j, are distinct. An order 2 Golomb ruler is a Golomb ruler such that all differences δijk` = |δk` − δij |, {i, j} 6 = {k, `}, are distinct as much as possible. Contruction of optimum order 2 Golomb ruler, i.e., of rulers of minimum length, is a highly combinatorial problem which has ...
متن کاملEnumeration of Golomb Rulers and Acyclic Orientations of Mixed Graphs
A Golomb ruler is a sequence of distinct integers (the markings of the ruler) whose pairwise differences are distinct. Golomb rulers, also known as Sidon sets and B2 sets, can be traced back to additive number theory in the 1930s and have attracted recent research activities on existence problems, such as the search for optimal Golomb rulers (those of minimal length given a fixed number of mark...
متن کاملGenetic Algorithm Approach to the Search for Golomb Rulers
GOLOMB RULERS Stephen W. Soliday soliday@gar eld.ncat.edu Abdollah Homaifar homaifar@gar eld.ncat.edu Department of Electrical Engineering North Carolina A&T State University Greensboro, North Carolina 27411 Gary L. Lebby lebby@gar eld.ncat.edu Abstract The success of genetic algorithm in nding relatively good solutions to NP-complete problems such as the traveling salesman problem and job-shop...
متن کاملAlgorithmic Aspects of Golomb Ruler Construction
We consider Golomb rulers and their construction. Common rulers feature marks at every unit measure, distances can often be measured with numerous pairs of marks. On Golomb rulers, for every distance there are at most two marks measuring it. The construction of optimal—with respect to shortest length for given number of marks or maximum number of marks for given length—is nontrivial, various pr...
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عنوان ژورنال:
- IEEE Trans. Information Theory
دوره 43 شماره
صفحات -
تاریخ انتشار 1997