Beyond Competitive Analysis
The competitive analysis of online algorithms has been criticized as being too crude and unrealistic. We propose refinements of competitive analysis in two directions: The first restricts the power of the adversary by allowing only certain input distributions, while the other allows for comparisons between information regimes for online decision-making. We illustrate the first with an application to the paging problem; as a byproduct we characterize completely the work functions of this important special case of the k-server problem. We use the second refinement to explore the power of lookahead in server and task systems.

title: On a network creation game
abstract: We introduce a novel game that models the creation of Internet-like networks by selfish node-agents without central design or coordination. Nodes pay for the links that they establish, and benefit from short paths to all destinations. We study the Nash equilibria of this game, and prove results suggesting that the "price of anarchy"  in this context (the relative cost of the lack of coordination) may be modest. Several interesting: extensions are suggested.

title: The serializability of concurrent database updates
abstract: A sequence of interleaved user transactions in a database system may not be ser:ahzable, t e, equivalent to some sequential execution of the individual transactions Using a simple transaction model, it ~s shown that recognizing the transaction histories that are serlahzable is an NP-complete problem. Several efficiently recognizable subclasses of the class of senahzable histories are therefore introduced; most of these subclasses correspond to senahzabdity principles existing in the hterature and used in practice Two new principles that subsume all previously known ones are also proposed Necessary and sufficient conditions are given for a class of histories to be the output of an efficient history scheduler, these conditions imply that there can be no efficient scheduler that outputs all of senahzable histories, and also that all subclasses of senalizable histories studied above have an efficient scheduler Finally, it is shown how these results can be extended to far more general transaction models, to transactions with partly interpreted functions, and to distributed database systems

title: The 1-Steiner Tree Problem
abstract: We present an O ( n 2 ) algorithm for finding the point on the plane which, if added to a given set of n points, will result in the shortest possible spanning tree.

title: On the Complexity of Database Queries
abstract: We revisit the issue of the complexity of database queries, in the light of the recent parametric refinement of complexity theory. We show that, if the query size (or the number of variables in the query) is considered as a parameter, then the relational calculus and its fragments (conjunctive queries, positive queries) are classified at appropriate levels of the so-called W hierarchy of Downey and Fellows. These results strongly suggest that the query size is inherently in the exponent of the data complexity of any query evaluation algorithm, with the implication becoming stronger as the expressibility of the query language increases. On the positive side, we show that this exponential dependence can be avoided for the extension of acyclic queries with ? (but not <) inequalities.

title: Optimization, approximation, and complexity classes
abstract: We define a natural variant of NP, MAX NP, and also a subclass called MAX SNP. These are classes of optimization problems, and in fact contain several natural, well-studied ones. We show that problems in these classes can be approximated with some bounded error. Furthermore, we show that a number of common optimization problems are complete under a kind of careful transformation (called L-reduction) that preserves approximability. It follows that such a complete problem has a polynomial-time approximation scheme iff the whole class does. These results may help explain the lack of progress on the approximability of a host of optimization problems.

title: On the approximability of trade-offs and optimal access of Web sources
abstract: We study problems in multiobjective optimization, in which solutions to a combinatorial optimization problem are evaluated with respect to several cost criteria, and we are interested in the trade-off between these objectives (the so-called Pareto curve). We point out that, under very general conditions, there is a polynomially succinct curve that /spl epsiv/-approximates the Pareto curve, for any /spl epsiv/>0. We give a necessary and sufficient condition under which this approximate Pareto curve can be constructed in time polynomial in the size of the instance and 1//spl epsiv/. In the case of multiple linear objectives, we distinguish between two cases: when the underlying feasible region is convex, then we show that approximating the multi-objective problem is equivalent to approximating the single-objective problem. If however the feasible region is discrete, then we point out that the question reduces to an old and recurrent one: how does the complexity of a combinatorial optimization problem change when its feasible region is intersected with a hyperplane with small coefficients; we report some interesting new findings in this domain. Finally, we apply these concepts and techniques to formulate and solve approximately a cost-time-quality trade-off for optimizing access to the World-Wide Web, in a model first studied by Etzioni et al. (1996) (which was actually the original motivation for this work).

title: Segmentation Problems

title: Topological queries in spatial databases
abstract: Handling spatial information is required by many database applications, and each poses different requirements on query languages. In many cases the precise size of the regions is important, while in other applications we may only be interested in the TOPOLOGICAL relations- hips between regions — intuitively, those that pertain to adjacency and connectivity properties of the regions, and are therefore invariant under homeomorphisms. Such differences in scope and emphasis are crucial, as they affect the data model, the query language, and performance. This talk focuses on queries targeted towards topological information for two- dimensional spatial databases, where regions are specified by polynomial inequalities with integer coeficients. We focus on two main aspects: (i) languages for expressing topological queries, and (ii) the representation of topological information. In regard to (i), we study several languages geared towards topological queries, building upon well-known topologi- cal relationships between pairs of planar regions proposed by Egenhofer. In regard to (ii), we show that the topological information in a spatial database can be precisely summarized by a finite relational database which can be viewed as a topological annotation to the raw spatial data. All topological queries can be answered using this annotation, called to- pological invariant. This yields a potentially more economical evaluation strategy for such queries, since the topological invariant is generally much smaller than the raw data. We examine in detail the problem of transla- ting topological queries against the spatial database into queries against the topological invariant. The languages considered are first-order on the spatial database side, and fixpoint and first-order on the topological in- variant side. In particular, it is shown that fixpoint expresses precisely the PTIME queries on topological invariants. This suggests that topolo- gical invariants are particularly well-behaved with respect to descriptive complexity. (Based on joint work with C.H.Papadimitriou, D. Suciu and L. Segoufin.

title: The complexity of recognizing polyhedral scenes
abstract: Given a drawing of straight lines on the plane, we wish to decide whether it is the projection of the visible part of a set of opaque polyhedra. Although there is an extensive literature and reports on empirically succesful algorithm: for this problem, there has been no definite result concerning its complexity. In this paper we show that, rather surprisingly, this problem is NP-complete. This is true even in the relatively simple case of trihedral scenes (no four planes share a point) without shadows or cracks. Despite this negative result, we present a fast algorithm for the important special case of orthohedral scenes (all planes are perpendicular to one of the three axes) with a fixed number of "possible" objects.

title: Reducibility among equilibrium problems
abstract: We address the fundamental question of whether the Nash equilibria of a game can be computed in polynomial time. We describe certain efficient reductions between this problem for normal form games with a fixed number of players and graphical games with fixed degree. Our main result is that the problem of solving a game for any constant number of players, is reducible to solving a 4-player game.