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We investigate the well-known anomalous diierences in the approximability properties of NP-complete optimization problems. We deene a notion of polynomial time reduction between optimization problems, and introduce conditions guaranteeing that such reductions preserve various types of approximate solutions. We then prove that a weighted version of the… (More)

- Patrik Floréen, Petteri Kaski, Jukka Kohonen, Pekka Orponen
- DIALM-POMC
- 2003

We consider the problem of maximizing the lifetime of a given multicast connection in a wireless network of energy-constrained (e.g. battery-operated) nodes, by choosing ideal transmission power levels for the nodes relaying the connection. We distinguish between two basic operating modes: In a <i>static</i> assignment, the power levels of the nodes are set… (More)

- Sakari Seitz, Mikko Alava, Pekka Orponen
- ArXiv
- 2005

A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the heuristic of focusing the local moves on the presently unsatisfied clauses is known to be very effective: the time to solution… (More)

- Pekka Orponen, Ker-I Ko, Uwe Schöning, Osamu Watanabe
- J. ACM
- 1994

We introduce a measure for the computational complexity of mdiwdual instances of a decision problem and study some of Its properties. The instance complexity of a string ~ with respect to a set A and time bound t, ict(x : A). is defined as the size of the smallest special-case program for A that run> m time t,decides x correctly, and makes no mistakes on… (More)

- Pekka Orponen
- Artif. Intell.
- 1990

We consider the complexity of combining bodies of evidence according to the rules of the Dempster{Shafer theory of evidence. We prove that, given as input a set of tables representing basic probability assignments m1; : : : ; mn over a frame of discernment , and a set A , the problem of computing the combined basic probability value (m1: : :mn)(A) is… (More)

- Mikko Alava, John Ardelius, +4 authors Sakari Seitz
- Proceedings of the National Academy of Sciences…
- 2008

We study the performance of stochastic local search algorithms for random instances of the K-satisfiability (K-SAT) problem. We present a stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by never going upwards in energy. ChainSAT is a focused algorithm in the sense that it focuses on variables occurring… (More)

- Pekka Orponen, Uwe Schöning
- Information and Control
- 1986

- Pekka Orponen, David A. Russo, Uwe Schöning
- SIAM J. Comput.
- 1986

- Jirí Síma, Pekka Orponen
- Neural Computation
- 2003

We survey and summarize the literature on the computational aspects of neural network models by presenting a detailed taxonomy of the various models according to their complexity theoretic characteristics. The criteria of classification include the architecture of the network (feedforward versus recurrent), time model (discrete versus continuous), state… (More)

- Patrik Floréen, Petteri Kaski, Jukka Kohonen, Pekka Orponen
- IEEE Journal on Selected Areas in Communications
- 2005

We consider the problem of maximizing the lifetime of a given multicast connection in a wireless network of energy-constrained (e.g., battery-operated) nodes, by choosing ideal transmission power levels for the nodes relaying the connection. We distinguish between two basic operating modes: In a static power assignment, the power levels of the nodes are set… (More)