We show that some basic linear control design problems are NP-hard, implying that, unless P=NP, they cannot be solved by polynomial time algorithms. The problems that we consider include simultaneous stabilization by output feedback, stabilization by state or output feedback in the presence of bounds on the elements of the gain matrix, and decentralized control. These results are obtained by fi...

We study single machine scheduling problems, where processing times of the jobs are exponential functions of their start times. For increasing functions, we prove strong NP-hardness of the makespan minimization problem with arbitrary job release times. For decreasing functions, maximum lateness minimization problem is proved to be strongly NP-hard and total weighted completion time minimization...

In many real-life situations, we only have partial information about probabilities. This information is usually described by bounds on moments, on probabilities of certain events, etc. – i.e., by characteristics c(p) which are linear in terms of the unknown probabilities pj . If we know interval bounds on some such characteristics ai ≤ ci(p) ≤ ai, and we are interested in a characteristic c(p),...

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with the presentation of a theoretical framework. Herein, three approximation algorithms are examined: linearprogramming relaxation, loopy-belief propagation, and a leaf-removal algorithm. T...

We discuss fast exponential time solutions for NP-complete problems. We survey known results and approaches, we provide pointers to the literature, and we discuss several open problems in this area. The list of discussed NP-complete problems includes the travelling salesman problem, scheduling under precedence constraints, satisfiability, knapsack, graph coloring, independent sets in graphs, ba...

The paper contributes to the systematic study (started by Berman and Karpinski) of explicit approximability lower bounds for small occurrence optimization problems. We present parametrized reductions for some packing and covering problems, including 3-Dimensional Matching, and prove the best known inapproximability results even for highly restricted versions of them. For example, we show that i...

NP-hard optimization problems have to be solved in practice. Since it is our belief that there are no efficient algorithms that always solve such problems, we seek for heuristic algorithms that perform well ”most of the time”. This brings up the important issue of how to evaluate the quality of heuristics. One common criteria is the approximation ratio which gives a worst case guarantee for the...

in this paper, a single machine sequencing problem is considered in order to find the sequence of jobs minimizing the sum of the maximum earliness and tardiness with idle times (n/1/i/etmax). due to the time complexity function, this sequencing problem belongs to a class of np-hard ones. thus, a special design of a simulated annealing (sa) method is applied to solve such a hard problem. to comp...

Although Knowledge Representation is full of reasoning problems that have been formally proved to be both NP-hard and coNP-hard, the experimental analysis has largely focused on problems belonging to either NP or coNP. We still do not know, for example, whether well-studied phenomena such as \phase transition", which show up for many NP-complete problems (e.g., sat) happen for p 2-complete prob...