{'fraction_non_alphanumeric': 0.024171888988361683, 'fraction_numerical': 0.009847806624888093, 'mean_word_length': 5.176795580110498, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Efficient Two-Dimensional Packing Algorithms for Mobile WiMAX

We present the result of research, developed within Nokia Siemens Networks, to solve the downlink sub-frame allocation problem in Mobile WiMAX (IEEE 802.16) technology in its full complexity, while simultaneously fulfilling real-life constraints on processing power and delay. We describe the IEEE 802.16 standard, and introduce two system models. A theoretical analysis of the two-dimensional packing problems originated by such models shows that they are both NP-hard in the strong sense. From a practical point of view, the processing budget for scheduling in the base station was estimated to be 1 ms on a state-of-the-art PC. Thus, we introduce two highly efficient heuristics that were developed to handle the system practically. A thorough computational analysis of their optimization characteristics and a system-level evaluation in realistic scenarios proved that the algorithms offer significant capacity gain in Mobile WiMAX systems that translate to increased operator revenues. 
 
This paper was accepted by Dimitris Bertsimas, optimization.