A k × n array with entries from the q-letter alphabet {0, 1, . . . , q − 1} is said to be t-covering if each k × t submatrix has (at least one set of) q distinct rows. We use the Lovász local lemma to obtain a general upper bound on the minimal number K = K(n, t, q) of rows for which a t-covering array exists; for t = 3 and q = 2, we are able to match the best-known such bound. Let Kλ = Kλ(n, t...

For a finite connected graph let be the spectral radius of its universal cover. We prove that for any graph of average degree and derive from it the following generalization of the Alon Boppana bound. If the average degree of the graph after deleting any radius ball is at least , then its second largest eigenvalue in absolute value is at least for some absolute constant . This result is tight i...

The main theorem states that if K is a finite CW-complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X×Sn for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial, then so is the action on X × Sn. Ünlü and Yalçın recently showed that any fi...

For any integer ρ ≥ 1 and for any prime power q, the explicit construction of a infinite family of completely regular (and completely transitive) q-ary codes with d = 3 and with covering radius ρ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius ρ,...

Due to the large volume of business process repositories, manually finding a particular process or a subset of them based on similarities in functionality or activities may become a difficult task. This paper presents a search method and a cluster method for business processes models. The search method considers linguistic and behavior information. The cluster method is based on covering arrays...

abstract one of the basic assumptions in hub covering problems is considering the covering radius as an exogenous parameter which cannot be controlled by the decision maker. practically and in many real world cases with a negligible increase in costs, to increase the covering radii, it is possible to save the costs of establishing additional hub nodes. change in problem parameters during the pl...

A covering array CA is a combinatorial structure specified as a matrix of N rows and k columns over an alphabet on v symbols such that for each set of t columns every t-tuple of symbols is covered at least once. Given the values of t, k, and v, the optimal covering array construction problem CAC consists in constructing a CA N; t, k, v with the minimum possible value of N. There are several rep...

The effective use of ASP solvers is essential for enhancing efficiency and scalability. The incidence matrix is a simple representation used in Constraint Programming (CP) and Integer Linear Programming for modeling combinatorial problems. Generating test cases for event-sequence testing is to find a sequence covering array (SCA). In this paper, we consider the problem of finding optimal sequen...