Intertemporal and Spatial Location of Disposal Facilities

Optimal capacity and location of a sequence of land.lls are studied, and the interactions between both decisions are pointed out.The decision capacity has some spatial implications, because it a.ects the feasible region for the rest of land.lls, and some temporal implications, because the capacity determines the lifetime of the land.ll and hence the instant of time where next land.lls will need to be constructed.Some general mathematical properties of the solution are provided and interpreted from an economic point of view.The resulting problem turns out to be no convex and therefore it can not be solved by conventional optimization techniques.Some global optimization methods are used to solve the problem in a particular case, in order to illustrate the behavior of the solution depending on parameter values.Landfilling;Optimal Capacity;Optimal Location;Global Optimization

Intertemporal and Spatial Location of Disposal Facilities

The optimal capacity and location of a sequence of landfills are studied, and the interactions between both decisions are pointed out. Deciding the capacity of a landfill has some spatial implications, because it effects the feasible region for the rest of the landfills, and some temporal implications because the capacity determines the lifetime of the landfill and hence the instant of time where the next landfills will need to be constructed. Some general mathematical properties of the solution are provided and interpreted from an economic point of view. The resulting problem turns out to be nonconvex and, therefore, it can not be solved by conventional optimization techniques. Some global optimization methods are used to solve the problem in a particular case to illustrate the behavior of the solution depending on the parameter values.Landfilling, Optimal Capacity, Optimal Location, Global Optimization.

Optimal Data Placement on Networks With Constant Number of Clients

We introduce optimal algorithms for the problems of data placement (DP) and page placement (PP) in networks with a constant number of clients each of which has limited storage availability and issues requests for data objects. The objective for both problems is to efficiently utilize each client's storage (deciding where to place replicas of objects) so that the total incurred access and installation cost over all clients is minimized. In the PP problem an extra constraint on the maximum number of clients served by a single client must be satisfied. Our algorithms solve both problems optimally when all objects have uniform lengths. When objects lengths are non-uniform we also find the optimal solution, albeit a small, asymptotically tight violation of each client's storage size by $\epsilon$lmax where lmax is the maximum length of the objects and $\epsilon$ some arbitrarily small positive constant. We make no assumption on the underlying topology of the network (metric, ultrametric etc.), thus obtaining the first non-trivial results for non-metric data placement problems

General Bounds for Incremental Maximization

We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value $k\in\mathbb{N}$ that grows over time, and we allow the solution to be extended one element at a time. We investigate the best-possible competitive ratio of such an incremental solution, i.e., the worst ratio over all $k$ between the incremental solution after $k$ steps and an optimum solution of cardinality $k$. We define a large class of problems that contains many important cardinality constrained maximization problems like maximum matching, knapsack, and packing/covering problems. We provide a general $2.618$-competitive incremental algorithm for this class of problems, and show that no algorithm can have competitive ratio below $2.18$ in general. In the second part of the paper, we focus on the inherently incremental greedy algorithm that increases the objective value as much as possible in each step. This algorithm is known to be $1.58$-competitive for submodular objective functions, but it has unbounded competitive ratio for the class of incremental problems mentioned above. We define a relaxed submodularity condition for the objective function, capturing problems like maximum (weighted) ($b$-)matching and a variant of the maximum flow problem. We show that the greedy algorithm has competitive ratio (exactly) $2.313$ for the class of problems that satisfy this relaxed submodularity condition. Note that our upper bounds on the competitive ratios translate to approximation ratios for the underlying cardinality constrained problems.Comment: fixed typo