Setting Parameters by Example

We introduce a class of "inverse parametric optimization" problems, in which one is given both a parametric optimization problem and a desired optimal solution; the task is to determine parameter values that lead to the given solution. We describe algorithms for solving such problems for minimum spanning trees, shortest paths, and other "optimal subgraph" problems, and discuss applications in multicast routing, vehicle path planning, resource allocation, and board game programming.Comment: 13 pages, 3 figures. To be presented at 40th IEEE Symp. Foundations of Computer Science (FOCS '99

Conflict-free star-access in parallel memory systems

We study conflict-free data distribution schemes in parallel memories in multiprocessor system architectures. Given a host graph G, the problem is to map the nodes of G into memory modules such that any instance of a template type T in G can be accessed without memory conflicts. A conflict occurs if two or more nodes of T are mapped to the same memory module. The mapping algorithm should: (i) be fast in terms of data access (possibly mapping each node in constant time); (ii) minimize the required number of memory modules for accessing any instance in G of the given template type; and (iii) guarantee load balancing on the modules. In this paper, we consider conflict-free access to star templates. i.e., to any node of G along with all of its neighbors. Such a template type arises in many classical algorithms like breadth-first search in a graph, message broadcasting in networks, and nearest neighbor based approximation in numerical computation. We consider the star-template access problem on two specific host graphs-tori and hypercubes-that are also popular interconnection network topologies. The proposed conflict-free mappings on these graphs are fast, use an optimal or provably good number of memory modules, and guarantee load balancing. (C) 2006 Elsevier Inc. All rights reserved

The Unreasonable Success of Local Search: Geometric Optimization

What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude $1/\epsilon^c$ is an approximation scheme for the following problems in the Euclidian plane: TSP with random inputs, Steiner tree with random inputs, facility location (with worst case inputs), and bicriteria $k$-median (also with worst case inputs). The randomness assumption is necessary for TSP

Design of Overlay Networks for Internet Multicast - Doctoral Dissertation, August 2002

Multicast is an efficient transmission scheme for supporting group communication in networks. Contrasted with unicast, where multiple point-to-point connections must be used to support communications among a group of users, multicast is more efficient because each data packet is replicated in the network – at the branching points leading to distinguished destinations, thus reducing the transmission load on the data sources and traffic load on the network links. To implement multicast, networks need to incorporate new routing and forwarding mechanisms in addition to the existing are not adequately supported in the current networks. The IP multicast are not adequately supported in the current networks. The IP multicast solution has serious scaling and deployment limitations, and cannot be easily extended to provide more enhanced data services. Furthermore, and perhaps most importantly, IP multicast has ignored the economic nature of the problem, lacking incentives for service providers to deploy the service in wide area networks. Overlay multicast holds promise for the realization of large scale Internet multicast services. An overlay network is a virtual topology constructed on top of the Internet infrastructure. The concept of overlay networks enables multicast to be deployed as a service network rather than a network primitive mechanism, allowing deployment over heterogeneous networks without the need of universal network support. This dissertation addresses the network design aspects of overlay networks to provide scalable multicast services in the Internet. The resources and the network cost in the context of overlay networks are different from that in conventional networks, presenting new challenges and new problems to solve. Our design goal are the maximization of network utility and improved service quality. As the overall network design problem is extremely complex, we divide the problem into three components: the efficient management of session traffic (multicast routing), the provisioning of overlay network resources (bandwidth dimensioning) and overlay topology optimization (service placement). The combined solution provides a comprehensive procedure for planning and managing an overlay multicast network. We also consider a complementary form of overlay multicast called application-level multicast (ALMI). ALMI allows end systems to directly create an overlay multicast session among themselves. This gives applications the flexibility to communicate without relying on service provides. The tradeoff is that users do not have direct control on the topology and data paths taken by the session flows and will typically get lower quality of service due to the best effort nature of the Internet environment. ALMI is therefore suitable for sessions of small size or sessions where all members are well connected to the network. Furthermore, the ALMI framework allows us to experiment with application specific components such as data reliability, in order to identify a useful set of communication semantic for enhanced data services