Packing and covering a tree by subtrees
Combinatorica
Extreme programming explained: embrace change
Extreme programming explained: embrace change
The Practical Guide to Extreme Programming
The Practical Guide to Extreme Programming
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Maximum Commonality Problems: Applications and Analysis
Management Science
A Comparison of Pair Versus Solo Programming Under Different Objectives: An Analytical Approach
Information Systems Research
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Motivated by applications in software programming, we consider the problem of covering a graph by a feasible labeling. Given an undirected graph G=(V,E), two positive integers k and t, and an alphabet @S, a feasible labeling is defined as an assignment of a set L"v@?@S to each vertex v@?V, such that (i) |L"v|@?k for all v@?V and (ii) each label @a@?@S is used no more than t times. An edge e={i,j} is said to be covered by a feasible labeling if L"i@?L"j0@?. G is said to be covered if there exists a feasible labeling that covers each edge e@?E. In general, we show that the problem of deciding whether or not a tree can be covered is strongly NP-complete. For k=2, t=3, we characterize the trees that can be covered and provide a linear time algorithm for solving the decision problem. For fixed t, we present a strongly polynomial algorithm that solves the decision problem; if a tree can be covered, then a corresponding feasible labeling can be obtained in time polynomial in k and the size of the tree. For general graphs, we give a strongly polynomial algorithm to resolve the covering problem for k=2, t=3.