Scheduling over Scenarios on Two Machines

We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all possible scenarios. Each scenario is a subset of jobs that must be executed in that scenario and all scenarios are given explicitly. The two objectives that we consider are minimizing the maximum makespan over all scenarios and minimizing the sum of the makespans of all scenarios. For both versions, we give several approximation algorithms and lower bounds on their approximability. With this research into optimization problems over scenarios, we have opened a new and rich field of interesting problems.Comment: To appear in COCOON 2014. The final publication is available at link.springer.co

Waterbodem- en palingpolluentenmeetnet: een tandem voor de waterbodemsanering

Within the sediment monitoring network from the Flemish Environmental Agency (VMM) the sediment quality of 600 locations in Flanders in both navigable as well as in unnavigable waters, is monitored by means of the TRIADE method. This TRIADE sediment quality assessment is based on a combination of chemical, biological and ecotoxicological parameters. The Research Institute for Nature and Forest (INBO) uses the Flemish eel pollutant monitoring network to monitor 350 locations in Flanders. These locations are situated on canals, rivers and on closed water bodies. The concentrations of PCBs, heavy metals and organochlorine pesticides are quantified in eel. At the same time these concentrations in eel give us valuable information on the bioavailability of these substances. Closer cooperation between both monitoring networks will provide an efficient policy tool, specifically for the sanitation/decontamination of the sediment and for the water policy in general. We will go into detail on the practical implications of such a kind of cooperation keeping in account the history, singularity and complementarity of both monitoring networks

Node-weighted Steiner tree and group Steiner tree in planar graphs

We improve the approximation ratios for two optimization problems in planar graphs. For node-weighted Steiner tree, a classical network-optimization problem, the best achievable approximation ratio in general graphs is Θ [theta] (logn), and nothing better was previously known for planar graphs. We give a constant-factor approximation for planar graphs. Our algorithm generalizes to allow as input any nontrivial minor-closed graph family, and also generalizes to address other optimization problems such as Steiner forest, prize-collecting Steiner tree, and network-formation games. The second problem we address is group Steiner tree: given a graph with edge weights and a collection of groups (subsets of nodes), find a minimum-weight connected subgraph that includes at least one node from each group. The best approximation ratio known in general graphs is O(log3 [superscript 3] n), or O(log2 [superscript 2] n) when the host graph is a tree. We obtain an O(log n polyloglog n) approximation algorithm for the special case where the graph is planar embedded and each group is the set of nodes on a face. We obtain the same approximation ratio for the minimum-weight tour that must visit each group

Improved Approximation Algorithms for (Budgeted) Node-weighted Steiner Problems

Moss and Rabani[12] study constrained node-weighted Steiner tree problems with two independent weight values associated with each node, namely, cost and prize (or penalty). They give an O(log n)-approximation algorithm for the prize-collecting node-weighted Steiner tree problem (PCST). They use the algorithm for PCST to obtain a bicriteria (2, O(log n))-approximation algorithm for the Budgeted node-weighted Steiner tree problem. Their solution may cost up to twice the budget, but collects a factor Omega(1/log n) of the optimal prize. We improve these results from at least two aspects. Our first main result is a primal-dual O(log h)-approximation algorithm for a more general problem, prize-collecting node-weighted Steiner forest, where we have (h) demands each requesting the connectivity of a pair of vertices. Our algorithm can be seen as a greedy algorithm which reduces the number of demands by choosing a structure with minimum cost-to-reduction ratio. This natural style of argument (also used by Klein and Ravi[10] and Guha et al.[8]) leads to a much simpler algorithm than that of Moss and Rabani[12] for PCST. Our second main contribution is for the Budgeted node-weighted Steiner tree problem, which is also an improvement to [12] and [8]. In the unrooted case, we improve upon an O(log^2(n))-approximation of [8], and present an O(log n)-approximation algorithm without any budget violation. For the rooted case, where a specified vertex has to appear in the solution tree, we improve the bicriteria result of [12] to a bicriteria approximation ratio of (1+eps, O(log n)/(eps^2)) for any positive (possibly subconstant) (eps). That is, for any permissible budget violation (1+eps), we present an algorithm achieving a tradeoff in the guarantee for prize. Indeed, we show that this is almost tight for the natural linear-programming relaxation used by us as well as in [12].Comment: To appear in ICALP 201

On the Maximum Crossing Number

Research about crossings is typically about minimization. In this paper, we consider \emph{maximizing} the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the maximum number of crossings of a geometric graph and that the weighted geometric case is NP-hard to approximate. We strengthen these results by showing hardness of approximation even for the unweighted geometric case and prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure

Magmatic evolution of the Nevado del Ruiz volcano, Central Cordillera, Colombia : mineral chemistry and geochemistry

A partir de nouvelles données pétrographiques, minéralogiques et géochimiques, les auteurs réalisent une caractérisation géochimique des laves du Nevado del Ruiz (éruptions quaternaires, historiques et récentes) et des formations volcaniques du Pliocène des pentes de la Cordillère central