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A minimum vertex cover is a vertex cover having the smallest possible number of vertices for a given graph. The size of a minimum vertex cover of a graph G is known as the ...

The process of finding a reduced set of basis vectors for a given lattice having certain special properties. Lattice reduction algorithms are used in a number of modern ...

The composite number problem asks if for a given positive integer N there exist positive integers m and n such that N=mn. The complexity of the composite number problem was ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

Informally, a function f is a one-way function if 1. The description of f is publicly known and does not require any secret information for its operation. 2. Given x, it is ...

A problem is assigned to the P (polynomial time) class if there exists at least one algorithm to solve that problem, such that the number of steps of the algorithm is bounded ...

Poisson's theorem gives the estimate (n!)/(k!(n-k)!)p^kq^(n-k)∼e^(-np)((np)^k)/(k!) for the probability of an event occurring k times in n trials with n>>1, p<<1, and np ...

Let A_n be the set of all sequences that contain all sequences {a_k}_(k=0)^n where a_0=1 and all other a_i=+/-1, and define c_k=sum_(j=0)^(n-k)a_ja_(j+k). Then the merit ...

The scramble number sn(G) of a graph G is a graph invariant developed to aid in the study of gonality of graphs. The scramble number is NP-hard to compute (Echavarria et al. ...

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...