Those who cannot remember the past, are condemned to repeat it." (Philosopher George Santayana) In this paper we show that keeping track of history enables significant improvements in the communication complexity of dynamic networks protocols. We improve the communication complexity for solving any graph problem from \Theta(E) to \Theta(V ), thus achieving the lower bound. Moreover, O(V ) is also our amortized complexity of solving any function (not only graph functions) defined on the local inputs of the nodes. This proves, for the first time, that amortized communication complexity, i.e. incremental cost of adapting to a single topology change, can be smaller than the communication complexity of solving the problem from scratch. This also has a practical importance: in real networks the topology and the local inputs of the nodes change.

!+ In this respect, one is interested in safe and cost-optimal dike heightenings for which the sum of the initial cost of investment and the future ~discounted! cost of maintenance is minimal+ For optimization purposes, a maintenance model has been developed for dikes subject to uncertain crest-level decline

Consider a system that performs a sequence of identical missions with breaks between missions. Suppose that maintenance can only be performed during these breaks and that limited time is available for performing maintenance actions. Selective maintenance refers to the process of identifying

; they are useful for browsing database structure, formulating queries, storing information such as statistics and sample values, and enabling query optimization. This paper presents the theoretical foundations of DataGuides along with an algorithm for their creation and an overview of incremental maintenance

In this paper, we show that keeping track of history enables significant improvements in the communication complexity of dynamic network protocols. We present a communication optimal maintenance of a spanning tree in a dynamic network. The amortized (on the number of topological changes) message

On a number theoretic property of optimal maintenance grouping A. van Harten, G.C. van Dijkhuizen & J.G.M. Mars

In this article we give an overview of the literature on multi-component maintenance optimization. We focus on work appearing since the 1991 survey A survey of maintenance models for multi-unit systems by Cho and Parlar (1991). This paper builds forth on the review article by Dekker et al. (1996

A well-studied problem in the electric power industry is that of optimally scheduling preventative maintenance of power generating units within a power plant. We show how these problems can be cast as constraint satisfaction problems and provide an "iterative learning" algorithm which

, either operational or failed. This research extends the previous models by developing an optimal maintenance policy for satellite constellations in which each satellite may operate in a finite number of degraded states. The constellation is assumed to consist of a finite number of satellites, each with a

are of use in this problem: FindPolicy determines an optimal main-tenance policy, while EvalPolicy allows a previously-determined policy to be evaluated according to a broad class of measures of effectiveness. These algorithms are applied to a hypothetical bridge facility, to determine and evaluate short