Abstract: Assume that each object in a database has m grades, or scores, one for each of m attributes. For example, an object can have a color grade, that tells how red it is, and a shape grade, that tells how round it is. For each attribute, there is a sorted list, which lists each object and its grade under that attribute, sorted by grade (highest grade first). There is some monotone aggregation function, orcombining rule, such as min or average, that combines the individual grades to obtain an overall grade. To determine the top k objects (that have the best overall grades), the naive algorithm must access every object in the database, to find its grade under each attribute. Fagin has given an algorithm (“Fagin’s Algorithm”, or FA) that is much more efficient. For some monotone aggregation functions, FA is optimal with high probability in the worst case. We analyze an elegant and remarkably simple algorithm (“the threshold algorithm”, or TA) that is optimal in a much stronger sense than FA. We show that TA is essentially optimal, not just for some monotone aggregation functions, but for all of them, and not just in a high-probability worst-case sense, but over every database. Unlike FA, which requires large buffers (whose size may grow unboundedly as the database size grows), TA requires only a small, constant-size buffer. TA allows early stopping, which yields, in a precise sense, an approximate version of the top k answers.

We introduce a natural variant of the (metric uncapacitated) k-median problem that we call the online median problem. Whereas the k-median problem involves optimizing the simultaneous placement of k facilities, the online median problem imposes the following additional constraints: the facilities are placed one at a time; a facility cannot be moved once it is placed, and the total number of facilities to be placed, k, is not known in advance. The objective of an online median algorithm is to minimize the competitive ratio, that is, the worst-case ratio of the cost of an online placement to that of an optimal offline placement. Our main result is a linear-time constant-competitive algorithm for the online median problem. In addition, we present a related, though substantially simpler, linear-time constant-factor approximation algorithm for the (metric uncapacitated) facility location problem. The latter algorithm is similar in spirit to the recent primal-dual-based facility location algorithm of Jain and Vazirani, but our approach is more elementary and yields an improved running time.

The Lemke--Howson algorithm is the classical algorithm for the problem NASH of finding one Nash equilibrium of a bimatrix game. It provides a constructive, elementary proof of existence of an equilibrium, by a typical "directed parity argument", which puts NASH into the complexity class PPAD. This paper presents a class of bimatrix games for which the Lemke--Howson algorithm takes, even in the best case, exponential time in the dimension d of the game, requiring #((# 3=4 ) d ) many steps, where # is the Golden Ratio. The "parity argument" for NASH is thus explicitly shown to be inefficient. The games are constructed using pairs of dual cyclic polytopes with 2d suitably labeled facets in d-space.

Abstract—Today’s reconfigurable hardware devices have huge densities and are partially reconfigurable, allowing for the configuration and execution of hardware tasks in a true multitasking manner. This makes reconfigurable platforms an ideal target for many modern embedded systems that combine high computation demands with dynamic task sets. A rather new line of research is engaged in the construction of operating systems for reconfigurable embedded platforms. Such an operating system provides a minimal programming model and a runtime system. The runtime system performs online task and resource management. In this paper, we first discuss design issues for reconfigurable hardware operating systems. Then, we focus on a runtime system for guaranteebased scheduling of hard real-time tasks. We formulate the scheduling problem for the 1D and 2D resource models and present two heuristics, the horizon and the stuffing technique, to tackle it. Simulation experiments conducted with synthetic workloads evaluate the performance and the runtime efficiency of the proposed schedulers. The scheduling performance for the 1D resource model is strongly dependent on the aspect ratios of the tasks. Compared to the 1D model, the 2D resource model is clearly superior. Finally, the runtime overhead of the scheduling algorithms is shown to be acceptably low. Index Terms—FPGA, partial reconfiguration, operating system, online scheduling, real-time. 1

We provide the first strongly polynomial algorithms with the best approximation ratio for all three variants of the unsplittable ow problem (UFP). In this problem we are given a (possibly directed) capacitated graph with n vertices and m edges, and a set of terminal pairs each with its own demand and profit. The objective is to connect a subset of the terminal pairs each by a single flow path as to maximize the total profit of the satisfied terminal pairs subject to the capacity constraints. Classical UFP, in which demands must be lower than edge capacities, is known to have an O( m) approximation algorithm. We provide the same result with a strongly polynomial combinatorial algorithm. The extended UFP case is when some demands might be higher than edge capacities. For that case we both improve the current best approximation ratio and use strongly polynomial algorithms.

Real-world networks often need to be designed under uncertainty, with only partial information and predictions of demand available at the outset of the design process. The field of stochastic optimization deals with such problems where the forecasts are specified in terms of probability distributions of future data. In this paper, we broaden the set of models as well as the techniques being considered for approximating stochastic optimization problems. For example, we look at stochastic models where the cost of the elements is correlated to the set of realized demands, and risk-averse models where upper bounds are placed on the amount spent in each of the stages. These generalized models require new techniques, and our solutions are based on a novel combination of the primal-dual method truncated based on optimal LP relaxation values, followed by a treerounding stage. We use these to give constant-factor approximation algorithms for the stochastic Steiner tree and single sink network design problems in these generalized models. 1.

We introduce a notion of universality in the context of optimization problems with partial information. Universality is a framework for dealing with uncertainty by guaranteeing a certain quality of goodness for all possible completions of the partial information set. Universal variants of optimization problems can be defined that are both natural and well-motivated. We consider universal versions of three classical problems: TSP, Steiner Tree and Set Cover. We present a polynomial-time algorithm to find a universal tour on a given metric space over vertices such that for any subset of the vertices, the sub-tour induced by the subset is within of an optimal tour for the subset. Similarly, we show that given a metric space over vertices and a root vertex, we can find a universal spanning tree such that for any subset of vertices containing the root, the sub-tree induced by the subset is within of an optimal Steiner tree for the subset. Our algorithms rely on a new notion of sparse partitions, that may be of independent interest. For the special case of doubling metrics, which includes both constant-dimensional Euclidean and growth-restricted metrics, our algorithms achieve an upper bound. We complement our results for the universal Steiner tree problem with a lower bound of that holds even for vertices on the plane. We also show that a slight generalization of the universal Steiner Tree problem is coNP-hard and present nearly tight upper and lower bounds for a universal version

In this paper we formally introduce a generic real-time multi-vehicle truckload pick-up and delivery problem. The problem includes the consideration of various costs associated with trucks ’ empty travel distances, jobs ’ delayed completion times, and job rejections. Although very simple, the problem captures most features of the operational problem of a real-world trucking fleet that dynamically moves truckloads between different sites according to customer requests that arrive continuously over time. We propose a mixed integer programming formulation for the off-line version of the problem. We then consider and compare five rolling horizon strategies for the real-time version. Two of the policies are based on a repeated reoptimization of various instances of the off-line problem, while the others use simpler local (heuristic) rules. One of the re-optimization strategies is new while the other strategies have recently been tested for similar real-time fleet management problems. The comparison of the policies is done under a general simulation framework. The analysis is systematic and consider varying traffic intensities, varying degrees of advance information, and varying degrees of flexibility for job rejection decisions. The new re-optimization policy is shown to systematically outperform the others under all these conditions.

In this paper, we study wireless network routing algorithms that use only short paths, for minimizing latency, and achieve good load balance, for balancing the energy use. We consider the special case when all the nodes are located in a narrow strip with width at most # 3/2 0.86 times the communication radius. We present algorithms that achieve good performance in terms of both measures simultaneously. In addition, our algorithms only use local information and can deal with dynamic change and mobility e#ciently. Keywords: wireless network, load-balanced routing, short path routing I.

this paper appeared in "Proceedings of the 32nd Annual ACM Symposium on Theory of Computing," Portland, OR, May 2000. 2 Current affiliation: Department of Computer Science, Princeton University, Princeton, NJ 08544. Most of this work was done while the author was at Stanford University and was visiting IBM Almaden Research Center. Research at Stanford was supported by the Pierre and Christine Lamond Fellowship, NSF Grant IIS-9811904.. and NSF Award CCR-9357849, with matching funds from. IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. 3 Most of this work was done while the Ruthor was visiting the IBM Almaden Research Center. 4 Supported in part by a David and Lucre Packard Foundation Fellowship, an A/fred P. Sloan Research Fellowship, an ONR Young Investigator Award, and NSF Faculty Early Career Development Award CCR-9701399