2011
DOI: 10.1007/978-3-642-18469-7_9
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Orthogonal Graph Drawing with Flexibility Constraints

Abstract: In this work we consider the following problem. Given a planar graph G with maximum degree 4 and a function flex : E −→ N 0 that gives each edge a flexibility. Does G admit a planar embedding on the grid such that each edge e has at most flex(e) bends? Note that in our setting the combinatorial embedding of G is not fixed.We give a polynomial-time algorithm for this problem when the flexibility of each edge is positive. This includes as a special case the problem of deciding whether G admits a drawing with at … Show more

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Cited by 14 publications
(48 citation statements)
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“…In particular, the construction of H does not use the hypothesis that H has at most two bends per edge, and therefore it can be applied without changes by starting from an e-constrained bend-minimum orthogonal representation H with one bend per edge, i.e., one verifying Property O1. Notice that such a property is still verified by H, due to Conditions (1) and (2). However, since in [13] an edge could have up two bends, the root child component µ could have one among the -, -, -, and -shape if µ is a P-or an R-node, and spirality ranging from 2 to 4 if µ is an S-node.…”
Section: Second Ingredientmentioning
confidence: 91%
See 1 more Smart Citation
“…In particular, the construction of H does not use the hypothesis that H has at most two bends per edge, and therefore it can be applied without changes by starting from an e-constrained bend-minimum orthogonal representation H with one bend per edge, i.e., one verifying Property O1. Notice that such a property is still verified by H, due to Conditions (1) and (2). However, since in [13] an edge could have up two bends, the root child component µ could have one among the -, -, -, and -shape if µ is a P-or an R-node, and spirality ranging from 2 to 4 if µ is an S-node.…”
Section: Second Ingredientmentioning
confidence: 91%
“…The data structure of Theorem 3.2, called Bend-Counter, is described in Section 5. We recall that the problem of computing orthogonal drawings of graphs with flexible edges is also studied by Bläsius et al [2,3], who however consider computational questions different from the ones in this paper. Theorem 3.2 is used in the proof of the following.…”
Section: Second Ingredientmentioning
confidence: 93%
“…Then its skeleton has only two embeddings E and E where E is obtained by flipping E. We have to show that the minimum over the two partial cost functions cost E H (·) and cost E H (·) remains convex. For the case that deg(s) + deg(t) = 5 the equation H = 2 holds and thus we only have to show convexity on the interval [2,3]. Obviously, cost H (·) is convex on this interval if and only if cost H (2) ≤ cost H (3).…”
Section: Lemma 6 If Theorem 5 Holds For Each Principal Split Componementioning
confidence: 99%
“…The result by Bläsius et al [2] concerning the problem FlexDraw takes this into account and additionally allows the user to control the final drawing, for example by allowing few bends on important edges. However, if such a drawing does not exist, the algorithm solving FlexDraw does not create a drawing at all and thus it cannot be used in a practical application.…”
Section: Introductionmentioning
confidence: 99%
“…Biedl and Kant [3] gave a linear-time algorithm for constructing an orthogonal drawing with at most two bends per edge of a graph with degree at most four (except for the octahedron -see Fig 1(b)). Bläsius et al [4] showed that it can be decided in polynomial time whether a planar graph has an embedding (i.e. a fixed cyclic ordering of the incident edges around each vertex) that allows an orthogonal drawing with at most one bend per edge.…”
Section: Introductionmentioning
confidence: 99%