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We suggest a graph-theoretic approach to steganography based on the idea of exchanging rather than overwriting pixels. We construct a graph from the cover data and the secret message. Pixels that need to be modified are represented as vertices and possible partners of an exchange are connected by edges. An embedding is constructed by solving the(More)
We present algorithms for the two layer straightline crossing minimization problem that are able to compute exact optima. Our computational results lead us to the conclusion that there is no need for heuristics if one layer is fixed, even though the problem is NP-hard, and that for the general problem with two variable layers, true optima can be computed(More)
A common method for drawing directed graphs is, as a rst step, to partition the vertices into a set of k levels and then, as a second step, to permute the vertices within the levels such that the number of crossings is minimized. We suggest an alternative method for the second step, namely, removing the minimal number of edges such that the resulting graph(More)
The data structure SPQR-tree represents the decomposition of a biconnected graph with respect to its triconnected components. SPQR-trees have been introduced by Di Battista and Tamassia [8] and, since then, became quite important in the field of graph algorithms. Theoretical papers using SPQR-trees claim that they can be implemented in linear time using a(More)
The Prize-Collecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears frequently in the design of utility networks where profit generating customers and the network(More)
Efficient subgraph queries in large databases are a time-critical task in many application areas as e.g. biology or chemistry, where biological networks or chemical compounds are modeled as graphs. The NP-completeness of the underlying subgraph isomorphism problem renders an exact subgraph test for each database graph infeasible. Therefore efficient methods(More)
The Prize-Collecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears in the design of utility networks (eg. fiber optics or district heating) where profit generating(More)
In automatic graph drawing a given graph has to be laid out in the plane, usually according to a number of topological and aesthetic constraints. Nice drawings for sparse nonplanar graphs can be achieved by determining a maximum planar subgraph and augmenting an embedding of this graph. This approach appears to be of limited value in practice, because the(More)