There Are No New Homometric Golomb Ruler Pairs with 12 Marks or Less
نویسندگان
چکیده
منابع مشابه
Algorithmic 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...
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 کاملEvolving Golomb Rulers
A Golomb Ruler is defined as a ruler that has marks unevenly spaced at integer locations in such a way that the distance between any two marks is unique. Unlike usual rulers, they have the ability to measure more discrete measures than the number of marks they possess. Although the definition of a Golomb Ruler does not place any restriction on the length of the ruler, researchers are usually in...
متن کاملGolomb Rulers
The Math Factor podcast posed the problem of finding the smallest number of inch marks on a 12 inch ruler so that one could still measure any integer length from 1 to 12. One needs only four additional marks besides 0 and 12; for example 1, 4, 7, 10 works. This entertaining problem lead to others during the next few minutes (you can listen at mathfactor.uark.edu/2005/10) and inspired us to look...
متن کاملA Constraint-Based Approach to the Golomb Ruler Problem
A Golomb ruler with m marks can be defined as a set of m distinct integers such that the differences between them are all distinct. An optimal Golomb ruler minimizes the value of the largest mark. The Golomb ruler problem is highly combinatorial and difficult to solve efficiently even for small sizes. Golomb rulers and related problems play an important role in, e.g., radio communication, VLSI ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Experimental Mathematics
دوره 3 شماره
صفحات -
تاریخ انتشار 1994