Abstract
Overlap graphs occur in computational biology and computer science, and have applications in genome sequencing, string compression, and machine scheduling. Given two strings $$s_{i}$$ s i and $$s_{j}$$ s j , their overlap string is defined as the longest string $$v$$ v such that $$s_{i} = uv$$ s i = u v and $$s_{j} = vw$$ s j = v w , for some non empty strings $$u,w$$ u , w , and its length is called the overlap between these two strings. A weighted directed graph is an overlap graph if there exists a set of strings with one-to-one correspondence to the vertices of the graph, such that each arc weight in the graph equals the overlap between the corresponding strings. In this paper, we characterize the class of overlap graphs, and we present a polynomial time recognition algorithm as a direct consequence. Given a weighted directed graph $$G$$ G , the algorithm constructs a set of strings that has $$G$$ G as its overlap graph, or decides that this is not possible.
Published Version
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