On the complexity of optimal homotopies

In this article, we provide new structural results and algorithms for the Homotopy Height problem. In broad terms, this problem quantifies how much a curve on a surface needs to be stretched to sweep continuously between two positions. More precisely, given two homotopic curves $\gamma_1$ and $\gamma_2$ on a combinatorial (say, triangulated) surface, we investigate the problem of computing a homotopy between $\gamma_1$ and $\gamma_2$ where the length of the longest intermediate curve is minimized. Such optimal homotopies are relevant for a wide range of purposes, from very theoretical questions in quantitative homotopy theory to more practical applications such as similarity measures on meshes and graph searching problems. We prove that Homotopy Height is in the complexity class NP, and the corresponding exponential algorithm is the best one known for this problem. This result builds on a structural theorem on monotonicity of optimal homotopies, which is proved in a companion paper. Then we show that this problem encompasses the Homotopic Fr\'echet distance problem which we therefore also establish to be in NP, answering a question which has previously been considered in several different settings. We also provide an O(log n)-approximation algorithm for Homotopy Height on surfaces by adapting an earlier algorithm of Har-Peled, Nayyeri, Salvatipour and Sidiropoulos in the planar setting

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

Progress and bottlenecks in the early domestication of the perennial oilseed Silphium integrifolium, a sunflower substitute

Silflower (Silphium integrifolium Michx.) is in the early stages of domestication as a perennial version of oilseed sunflower, its close relative. Grain crops with deep perennial root systems will provide farmers with new alternatives for managing soil moisture and limiting or remediating soil erosion, fertilizer leaching, and loss of soil biota. Several cycles of selection for increased seed production potential following initial germplasm evaluation in 2002 have provided opportunities to document the botany and ecology of this relatively obscure species, to compare agronomic practices for improving its propagation and management, and to evaluate the differences between semi-domesticated and wild accessions that have accrued over this time through intentional and unintentional genetic processes. Key findings include: domestication has increased aboveground biomass at seedling and adult stages; seed yield has increased more, achieving modest improvement in harvest index. Harvest index decreases with nitrogen fertilization. Silflower acquires nitrogen and water from greater depth than typical crops. In agricultural silflower stands within its native range, we found that Puccinia silphii (rust) and Eucosma giganteana (moth) populations build up to unacceptable levels, but we also found genetic variation for traits contributing to resistance or tolerance. Breeding or management for reduced height and vegetative plasticity should be top priorities for future silflower research outside its native range.Fil: Vilela, Alejandra Elena. Museo Paleontológico Egidio Feruglio; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: González Paleo, Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Museo Paleontológico Egidio Feruglio; ArgentinaFil: Turner, Kathryn. The Land Institute; Estados UnidosFil: Peterson, Kelsey. The Land Institute; Estados UnidosFil: Ravetta, Damián Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Museo Paleontológico Egidio Feruglio; ArgentinaFil: Crews, Timothy E.. The Land Institute; Estados UnidosFil: Van Tassel, David. The Land Institute; Estados Unido