This paper continues the investigation of the connection between proof systems and approximation. The emphasis is on proving tight non-approximability results via consideration of measures like the "free bit complexity" and the "amortized free bit complexity" of proof systems.

This study focuses on the routing and Wavelength-Assignment (RWA) problem in wavelength-routed optical WDM networks. Most of the attention is devoted to such networks operating under the wavelength-continuity constraint, in which lightpaths are set up for connection requests between node pairs, and a single lightpath must occupy the same wavelength on all of the links that it spans. In setting up a lightpath, a route must be selected and a wavelength must be assigned to the lightpath. If no wavelength is available for this lightpath on the selected route, then the connection request is blocked. We examine the RWA problem and review various routing approaches and wavelengthassignment approaches proposed in the literature. We also briefly consider the characteristics of wavelength-converted networks (which do not have the wavelength-continuity constraint), and we examine the associated research problems and challenges. Finally, we propose a new wavelengthassignment scheme, called Distributed Relative Capacity Loss (DRCL), which works well in distributed-controlled networks, and we demonstrate the performance of DRCL through simulation. 1

... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400-variable 3-SAT problems in about 2 hours on the average. In general, it can solve hard n-variable random 3-SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NP-complete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.

The timetabling problem consists in fixing a sequence of meetings between teachers and students in a prefixed period of time (typically a week), satisfying a set of constraints of various types. A large number of variants of the timetabling problem have been proposed in the literature, which differ from each other based on the type of institution involved (university or high school) and the type of constraints. This problem, that has been traditionally considered in the operational research field, has recently been tackled with techniques belonging also to artificial intelligence (e.g. genetic algorithms, tabu search, simulated annealing, and constraint satisfaction). In this paper, we survey the various formulations of the problem, and the techniques and algorithms used for its solution.

This paper presents a new algorithm for dynamic routing of bandwidth guaranteed tunnels where tunnel routing requests arrive one-by-one and there is no a priori knowledge regarding future requests. This problem is motivated by service provider needs for fast deployment of bandwidth guaranteed services and the consequent need in backbone networks for fast provisioning of bandwidth guaranteed paths. Offline routing algorithms cannot be used since they require a priori knowledge of all tunnel requests that are to be routed. Instead, on-line algorithms that handle requests arriving one-by-one and that satisfy as many potential future demands as possible are needed. The newly developed algorithm is an on-line algorithm and is based on the idea that a newly routed tunnel must follow a route that does not "interfere too much" with a route that may be critical to satisfy a future demand. We show that this problem is NP-hard. We then develop a path selection heuristic that is based on the idea ...

. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...

. Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions.

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The following packing problem arises in connection with lettering of maps: Given n distinct points pl, p2,.... pn in the plane, determine the supremum uoPi of all reals U, such that there are n pan-wise dtsjomt, axis-parallel, closed squares Ql, Q2,.... Qn of side-length u, where each pi ts a corner of Qi. Note that — by using afine transformation — the problem is equivalent to the case when we want largest homothetic cop~es of a jized rectangle or parallelogram tnstead of equal ly-szzed squares. In the cartographic application, the points are items (groundwater-drillho les etc.) and the squares are places for labels associated with these items (sulphate concentration etc.). An algorithm is presented, that in O(n log n] time either produces a solution, that is guaranteed to be at least half as large as the supremum. This is optimal, m the sense that the corresponding decision problem is NP-complete, no po[ynomzal approximation algorithm with a guaranteed factor ezceedmg ~ exwts, provided that P # AfP; and there M also a lower bound of C2(n log n) for the running time. 1

We survey the theoretical results obtained for wavelength routing in all–optical networks, present some new results and propose several open problems. In all–optical networks the vast bandwidth available is utilized through wavelength division multiplexing: a single physical optical link can carry several logical signals, provided that they are transmitted on different wavelengths. The information, once transmitted as light, reaches its destination without being converted to electronic form in between, thus reaching high data transmission rates. We consider both networks with arbitrary topologies and particular networks of practical interest.