By Nikhil Bansal (auth.), Thomas Erlebach, Giuseppe Persiano (eds.)
This booklet constitutes the completely refereed put up workshop lawsuits of the tenth overseas Workshop on Approximation and on-line Algorithms, WAOA 2012, held in Ljubljana, Slovenia, in September 2012 as a part of the ALGO 2012 convention occasion. The 22 revised complete papers offered including invited speak have been conscientiously reviewed and chosen from 60 submissions. The workshop coated parts similar to geometric difficulties, on-line algorithms, scheduling, algorithmic online game conception, and approximation algorithms.
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Extra info for Approximation and Online Algorithms: 10th International Workshop, WAOA 2012, Ljubljana, Slovenia, September 13-14, 2012, Revised Selected Papers
In some sense this compensates the negative eﬀect of “multiple counting”. Lemma 7. Let e be a critical edge and let e∗ be an edge in T ∗ that is not adjacent to e. If the 1-ﬂip replacing e with e∗ is feasible then both endpoints of e∗ are forward nodes in T . Proof. Let e = (u, v) and let e∗ = (x, y). Since e and e∗ are not adjacent and the 1-ﬂip replacing e with e∗ is feasible the T -path connecting x and y contains u, v as interior nodes. Hence u and v are not leaves in T . g. that u is unprocessed and hence cubic.
We denote such low-degree nodes as path nodes, as they are exactly the nodes that arise in paths, and consequently call this reformulation maximum path-node spanning tree (MPST). Although the original and our formulation of the problem lead to the same optimum solutions (and have the same practical applications), ours is more appropriate for analyzing approximation algorithms. In fact, every spanning tree is a 1/2-approximation for MPST since at least half the nodes have degree 1 or 2. Notice that complementary problem formulations have also been successfully considered in the context of similar optimization problems.
In later works [4,5], suﬃcient density conditions for the existence of spanning spiders—spanning trees with at most one branch node—are considered. Salamon  gives a diﬀerent practical motivation for MBST, which is also based on optical networks. Moreover, he provides logarithmic upper bounds on the required number of branch nodes depending on the total number of nodes and the density of the input graph. Cerulli et al.  develop ILP formulations for MBST which allows them to solve small instance to optimality.