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https://doi.org/10.1007/978-3-7091-3721-5lgorithms from classical graph theory, and for algorithms implemented on networks of communicating processors and distributed systems. Moreover, this theory gives an algebraic model which allows us to mathematically prove properties of distributed algorithms.
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https://doi.org/10.1007/978-1-349-18070-7in be generated by a hyperedge-replacement grammar. Because many familiar graph-theoretic properties like connectedness, .-colorability, planarity, the existence of Eulerian and Hamiltonian paths and cycles, etc. are compatible and compatibility is closed under Boolean operations, the members of a h
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https://doi.org/10.1007/978-3-031-47884-0or (1) we propose grid embeddings of graphs and measure ”nice” by algorithmic cost measures of the embeddings, e.g., area, expansion, edge length, etc. For (2) we prove that optimal embeddings with fixed costs are NP-complete, even for binary trees. This sharpens previous NP-completeness results of
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https://doi.org/10.1007/978-3-031-31104-8rected distance graph with groups of required vertices and Steiner vertices, find a shortest connected subgraph containing at least one required vertex of each group. We propose two efficient approximation algorithms computing different approximate solutions in time .(|.| + |.|log|.|) and in time .(
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https://doi.org/10.1007/978-3-031-31111-6thm which requires O(n.) time. However, in the average case, C.(G) is computed by this algorithm for almost all integers k (in the asymptotic sense) with O ≦ k ≦ 2n − 2 in O(n.) time. We next present a parallel algorithm which requires O(n. log n) time. In the average case, this algorithm computes C
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