text: This article examines dynamic energy consumption caused by data during software execution on deeply embedded microprocessors, which can be significant on some devices. In worst-case energy consumption analysis, energy models are used to find the most costly execution path. Taking each instruction’s worst-case energy produces a safe but overly pessimistic upper bound. Algorithms for safe and tight bounds would be desirable. We show that finding exact worst-case energy is NP-hard, and that tight bounds cannot be approximated with guaranteed safety. We conclude that any energy model targeting tightness must either sacrifice safety or accept overapproximation proportional to data-dependent energy.
  @cite_9: Simple, polynomial-time, heuristic algorithms for finding approximate solutions to various polynomial complete optimization problems are analyzed with respect to their worst case behavior, measured by the ratio of the worst solution value that can be chosen by the algorithm to the optimal value. For certain problems, such as a simple form of the kanpsack problem and an optimization problem based on satisfiability testing, there are algorithms for which this ratio is bounded by a constant, independent of the problem size. For a number of set covering problems, simple algorithms yield worst case ratios which can grow with the log of the problem size. And for the problem of finding the maximum clique in a graph, no algorithm has been found for which the ratio does not grow at least as fast as n^@e, where n is the problem size and @e>0 depends on the algorithm.
summary: Formally, following the presentation of @cite_9 , define @math to be a set of literals, and @math a set of disjunctive form clauses: where each @math is a Boolean variable. A truth assignment defines each @math or its negation to be true. A clause is deemed to be satisfied if at least one literal in the clause is assigned true. A MAXSAT problem is a set of literals and set of clauses @math , such that the solution is the truth assignment that causes the maximal number of clauses to be satisfied.