Low Earth Orbit (LEO) satellites face critical energy constraints when performing onboard computation during Earth's umbra periods. While task migration to illuminated satellites mitigates battery stress, it introduces a trade-off between migration frequency and energy cost. This paper investigates the energy-efficient task migration problem for LEO satellite constellations subject to umbra constraints. We formally formulate this problem as a mixed-integer nonlinear programming (MINLP) model, which captures the complex trade-offs among energy consumption, computational load, and inter-satellite communication constraints under umbra conditions. To address this challenge, we propose a Score-based Priority Satellite Task Migration with Dynamic Programming (SPTD) algorithm that optimizes total energy consumption by assigning priority to candidate satellites based on their remaining energy capacity, computational capacity, and inter-satellite link bandwidth. Extensive simulations demonstrate that SPTD achieves significantly lower total energy consumption compared to state-of-the-art migration strategies, with performance approaching the theoretical optimum. The results validate the algorithm's effectiveness across varying constellation scales, providing a foundation for sustainable operation of future LEO satellite computing infrastructure.

Edge native applications usually consist of several dependent tasks encapsulated in containers and started on-demand in the edge cloud. Unfortunately, the application performance is deeply affected by the notorious cold startup problem of containers. Pre-warming Zygote container pre-imported certain common packages has been proven as an effective startup acceleration solution. Since a Zygote can be shared among colocated tasks that require identical common packages, not only the Zygote planning but also the task scheduling decisions shall be carefully made to maximize the benefit of the Zygotes pre-warmed in limited memory. Additionally, task dependency necessitates co-locating highly dependent tasks on the same server, naturally raising a dilemma in task scheduling. To this end, in this paper, we investigate the problem of how to plan Zygote and schedule tasks for application completion time minimization, which is proved to be NP-hard. We further propose a Priority and Popularity (P&P) based edge native application acceleration algorithm. Both theoretical analysis and extensive experiments demonstrate the effectiveness of our proposed algorithm. The experiment results show that P&P can reduce the application completion time by 11.7%.