We present a randomized on-line algorithm for the Metrical Tti System problem that achieves a competitive ratio of O(log6 n) for arbitrary metric spaces, against art oblivious adversary. This is the first algorithm to achieve a sublinear competitive ratio for all mernc spaces. Our algorithm uses a recent result of Bart.al[Bar96] thatan arbitrarymetric space can be probabilistically approximated by a set of metric spaces called "k-hierarchical well-separated trees" (k-HST'S). Indeed, the main technical result of this paper is an 0(}og2 n)-competitive algorithm for fl(log2 n)-HST spaces. This, combined with the result of [Bar96], yields the general bound.Note that for the k-server problem on metric spaces of k + c points our result implies a competitive ratio of O(C6 log6 k).

The problem of combining expert advice, studied extensively in the Computational Learning Theory literature, and the Metrical Task System (MTS) problem, studied extensively in the area of On-line Algorithms, contain a number of interesting similarities. In this paper we explore the relationship between these problems and show how algorithms designed for each can be used to achieve good bounds and new approaches for solving the other. Specific contributions of this paper include: • An analysis of how two recent algorithms for the MTS problem can be applied to the problem of tracking the best expert in the "decision-theoretic" setting, providing good bounds and an approach of a much different flavor from the well-known multiplicative-update algorithms. • An analysis showing how the standard randomized Weighted Majority (or Hedge) algorithm can be used for the problem of "combining on-line algorithms on-line", giving much stronger guarantees than the results of Azar, Y., Broder, A., & Manasse, M. (1993). Proc ACM-SIAM Symposium on Discrete Algorithms (pp. 432-440) when the algorithms being combined occupy a state space of bounded diameter. • A generalization of the above, showing how (a simplified version of) Herbster and Warmuth's weight-sharing algorithm can be applied to give a "finely competitive" bound for the uniform-space Metrical Task System problem. We also give a new, simpler algorithm for tracking experts, which unfortunately does not carry over to the MTS problem. Finally, we present an experimental comparison of how these algorithms perform on a process migration problem, a problem that combines aspects of both the experts-tracking and MTS formalisms.

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We construct an online algorithm for paging that achieves an Or + log k competitive ratio when compared to an offline strategy that is allowed the additional ability to "rent" pages at a cost of 1=r. In contrast, the competitive ratio of the Marking algorithm for this scenario is Or log k. Our algorithm can be thought of in the standard setting as having a "fine-grained" competitive ratio, achieving an O1 ratio when the request sequence consists of a small number of working sets, gracefully decaying to Olog k as this number increases. Our result is a generalization of the result in Bartal et al. [2] that one can achieve an Or + logn ratio for the unfair n-state uniform-space Metrical Task System problem. That result was a key component of the polylogn competitive randomized algorithm given in that paper for the general Metrical Task System problem. One motivation of this work is that it may be a first step toward achieving a polylogk randomized competitive ratio for the much more difficult k-server problem.

Logisim enables students in introductory courses to design and simulate logic circuits. The program's design emphasizes simplicity of use, with a secondary goal of enabling design of sophisticated circuits. This motivates a two-tiered system, where users can move to the second tier by selecting a menu option.Users draw circuits of logic gates using the toolbox model popular in drawing programs. The circuit automatically propagates circuit values through the circuit; by selecting the appropriate tool, users can toggle switches to see how the circuit behaves in other situations. In the advanced tier, the user can treat circuits as black boxes within larger circuits, enabling the simulation of hierarchical designs. The author has successfully drawn and tested a simple 8 bit CPU using the program.The program has proven useful in a variety of introductory courses, from a nonmajors survey course to a sophomore-level systems course. Students find Logisim simple to follow, and find the laboratories designed around it useful in reinforcing the circuit concepts from class.In this article, we identify and compare a variety of systems similar to Logisim, we explore Logisim's features in detail, and we examine its use in class assignments.

Abstract. The problem of combining expert advice, studied extensively in the Computational Learning Theory literature, and the Metrical Task System (MTS) problem, studied extensively in the area of On-line Algorithms, contain a number of interesting similarities. In this paper we explore the relationship between these problems and show how algorithms designed for each can be used to achieve good bounds and new approaches for solving the other. Specific contributions of this paper include:• An analysis of how two recent algorithms for the MTS problem can be applied to the problem of tracking the best expert in the "decision-theoretic" setting, providing good bounds and an approach of a much different flavor from the well-known multiplicative-update algorithms.• An analysis showing how the standard randomized Weighted Majority (or Hedge) algorithm can be used for the problem of "combining on-line algorithms on-line", giving much stronger guarantees than the results of Azar, Y., Broder, A., & Manasse, M. (1993). Proc ACM-SIAM Symposium on Discrete Algorithms (pp. 432-440) when the algorithms being combined occupy a state space of bounded diameter.• A generalization of the above, showing how (a simplified version of) Herbster and Warmuth's weight-sharing algorithm can be applied to give a "finely competitive" bound for the uniform-space Metrical Task System problem. We also give a new, simpler algorithm for tracking experts, which unfortunately does not carry over to the MTS problem.Finally, we present an experimental comparison of how these algorithms perform on a process migration problem, a problem that combines aspects of both the experts-tracking and MTS formalisms.

Over the last ten years, our department's breadth-first introductory course has evolved independently of other survey courses in computer science. Due to its success, we duplicated the ideas into our course for non-majors, and this has also proven successful. None of the published resources match our vision for these courses, and so the department has developed its own. In this paper, we describe the design of the majors course, and we introduce a variety of resources developed for both courses. These resources, which could be useful in many other courses also, are freely available through the Web.

Over the last ten years, our department's breadth-first introductory course has evolved independently of other survey courses in computer science. Due to its success, we duplicated the ideas into our course for non-majors, and this has also proven successful. None of the published resources match our vision for these courses, and so the department has developed its own. In this paper, we describe the design of the majors course, and we introduce a variety of resources developed for both courses. These resources, which could be useful in many other courses also, are freely available through the Web.