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In future generation networks, various access technologies, such as Wi-Fi, Bluetooth, GPRS and UMTS, etc., are simultaneously available to mobile devices. They vary in characteristics (communication range, power consumption, security, etc.) and QoS parameters (bandwidth, delay, etc.) The notion of always best connected (ABC) enables people to run applications over the most efficient combination of access technologies with continuous connectivity. Access selection is the key functional block in ABC solutions, as it chooses the most suitable access networks for application traffic flows. However, it is important that access selection decisions be dynamically made, minimizing the power consumption on mobile devices while satisfying QoS requirements and user/application preferences. In this paper, we model the problem of multi-constraint dynamic access selection (MCDAS) as a variant of bin packing problem. A series of approximation algorithms derived from the first fit decreasing (FFD) algorithm are proposed for finding near-optimal solutions. Simulation studies show that the algorithms we propose gradually improve performance towards quasi-optimal solutions in terms of power consumption and preference satisfaction.