By Alfredo Ferro, Fabrizio Luccio, Peter Widmayer

This publication constitutes the refereed court cases of the seventh overseas convention, enjoyable 2014, held in July 2014 in Lipari Island, Sicily, Italy.

The 29 revised complete papers have been conscientiously reviewed and chosen from forty nine submissions. They function a wide number of subject matters within the box of the use, layout and research of algorithms and knowledge constructions, targeting effects that supply fun, witty yet still unique and scientifically profound contributions to the world. particularly, algorithmic questions rooted in biology, cryptography, video game thought, graphs, the net, robotics and mobility, combinatorics, geometry, stringology, in addition to space-conscious, randomized, parallel, disbursed algorithms and their visualization are addressed.

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Additional info for Fun with Algorithms: 7th International Conference, FUN 2014, Lipari Island, Sicily, Italy, July 1-3, 2014. Proceedings

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Similarly if S is horizontal, the direction of the right edge is defined by the constraint and we give direction to the bottom edge so that the right-bottom vertex is either a source or a sink. We thus have an orientation of the edges of H satisfying all the constraints at the end of the traversal. It is easy to see that this orientation defines a directed acyclic graph. For a contradiction assume that there is a directed cycle C in H. Then take the bottommost vertex x of C which is to the right of every other bottommost vertex.

L(e1 ) = l(e2 ) or l(e3 ) = l(e4 ). 2. l(e0 ) = N and c(w1 ) < c(w2 ) if and only if c(w3 ) < c(w4 ). 3. l(e0 ) = F and c(w1 ) < c(w2 ) if and only if c(w3 ) > c(w4 ). The following lemma shows that if c is extendible with respect to l, then there is a (3k + 1, k)-threshold-coloring of G6 ; see [1] for the proof. Lemma 5. Consider the graph G6 in Fig. 6(a). Let l : E → {N, F } be an edge labeling of E and let c : (V − {u, v}) → {k + 2, . . , 2k + 1} be an extendible coloring with respect to l.

LNCS, vol. 1665, pp. 350–363. Springer, Heidelberg (1999) 9. : Systems of distant representatives. Discrete Applied Mathematics 145(2), 306–316 (2005) 10. : Graph sandwich problems. Journal of Algorithms 19(3), 449–473 (1995) 11. : Labelling graphs with a condition at distance 2. SIAM Journal on Discrete Mathematics 5(4), 586–595 (1992) 12. : Difference graphs. Discrete Applied Mathematics 28(1), 35–44 (1990) 13. : Threshold Graphs and Related Topics. North-Holland (1995) 14. : From garbage to rainbows: Generalizations of graph coloring and their applications.

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