On a communication complexity problem in combinatorial number theory
نویسندگان
چکیده
The original knapsack problem is well known to be NP-complete. In a multidimensional version one have decide whether $p\in \N^k$ in sumset-sum of set $X \subseteq or not. this paper we are going investigate communication complexity related this.
منابع مشابه
On a Combinatorial Problem in Number Theory
1. Introduction One of the problems mentioned injl] (on p. 187) concerns the estimation of the magnitude of the largest number g(N) such that, from every sequence of N distinct natural numbers, one can always select a subsequence of g{N) integers with the property that no sum of two distinct integers of this subsequence belongs to the original sequence. It should be mentioned that the function ...
متن کاملOn a Problem in Elementary Number Theory and a Combinatorial Problem
(1) f~(n) < exp [(log n) 1 /2 ]E Recently, I observed that using a combinatorial theorem due to Rado and myself (1) can be considerably improved and it might, in fact, be possible to obtain the correct order of magnitude for f 1 (n) . The combinatorial theorem in question states as follows [2] : Let g(k, t) be the smallest integer so that if A 1 , • • • , A 8 , s = g(k, t), are sets each having...
متن کاملOn a Combinatorial Problem in Group Theory
Let n be a positive integer or infinity (denote ∞). We denote by W ∗(n) the class of groups G such that, for every subset X of G of cardinality n + 1, there exist a positive integer k, and a subset X0 ⊆ X, with 2 ≤ |X0| ≤ n + 1 and a function f : {0, 1, 2, . . . , k} −→ X0, with f(0) 6= f(1) and non-zero integers t0, t1, . . . , tk such that [x0 0 , x t1 1 , . . . , x tk k ] = 1, where xi := f(...
متن کاملCombinatorial Number Theory
Background. The integer distance graph G(Z, D) with distance set D = {d1, d2, . . .} has the set of integers Z as the vertex set and two vertices x, y ∈ Z are adjacent if and only if |x − y| ∈ D. The integer distance graphs (under Euclidean norm) were first systematically studied by Eggleton–Erdős–Skilton in 1985 [12, 13], and have been investigated in many ways [50, 56, 57, 61]. One of main go...
متن کاملGroups in Combinatorial Number Theory
In combinatorial number theory, there are many topics related to group structure. Even for abelian or cyclic groups, there are some very challenging unsolved conjectures. In this talk we give a survey of problems, results and methods in several fields of combinatorial number theory. The topics include sumsets in additive combinatorics, Snevily’s conjecture and Latin transversals, covers of the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Moscow journal of combinatorics and number theory
سال: 2021
ISSN: ['2640-7361', '2220-5438']
DOI: https://doi.org/10.2140/moscow.2021.10.297