This paper studies the design of self-adjusting networks whose topology dynamically adapts to the workload, in an online and demand-aware manner. This problem is motivated by emerging optical technologies which allow to reconfigure the datacenter topology at runtime. Our main contribution is ReNet, a self-adjusting network which maintains a balance between the benefits and costs of reconfigurations. In particular, we show that ReNets are statically optimal for arbitrary sparse communication demands, i.e., perform at least as good as any fixed demand-aware network designed with a perfect knowledge of the future demand. Furthermore, ReNets provide compact and local routing, by leveraging ideas from self-adjusting datastructures.
Indeed, the physical topology is the next frontier in an ongoing effort to render communication networks more flexible and reconfigurable. Over the last years, reconfigurable technologies (typically software) already enabled various innovations in important domains such as traffic engineering @cite_10 @cite_23 , load-balancing @cite_11 @cite_6 , and switching @cite_9 @cite_68 .
@cite_9 @cite_6 @cite_23 @cite_68 @cite_10 @cite_11
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Emerging communication technologies allow to reconfigure the physical network topology at runtime, enabling demand-aware networks (DANs): networks whose topology is optimized toward the workload they serve. However, today, only little is known about the fundamental algorithmic problems underlying the design of such demand-aware networks. This paper presents the first bounded-degree, demand-aware network, ct-DAN, which minimizes both congestion and route lengths. The designed network is provably (asymptotically) optimal in each dimension individually: we show that there do not exist any bounded-degree networks providing shorter routes (independently of the load), nor do there exist networks providing lower loads (independently of the route lengths). The main building block of the designed ct-DAN networks are ego-trees: communication sources arrange their communication partners in an optimal tree, individually. While the union of these ego-trees forms the basic structure of cl-DANs, further techniques are presented to ensure bounded degrees (for scalability). To date, topology control in wireless ad hoc and sensor networks--the study of how to compute from the given communication network a subgraph with certain beneficial properties .has been considered as a static problem only; the time required to actually schedule the links of a computed topology without message collision was generally ignored. In this paper we analyze topology control in the context of the physical Signal-to-Interference-plus-Noise-Ratio (SINR) model, focusing on the question of how and how fast the links of a resulting topology can actually be realized over time.For this purpose, we define and study a generalized version of the SINR model and obtain theoretical upper bounds on the scheduling complexity of arbitrary topologies in wireless networks. Specifically, we prove that even in worst-case networks, if the signals are transmitted with correctly assigned transmission power levels, the number of time slots required to successfully schedule all links of an arbitrary topology is proportional to the squared logarithm of the number of network nodes times a previously defined static interference measure Interestingly, although originally considered without explicit accounting for signal collision in the SINR model, this static interference measure plays an important role in the analysis of link scheduling with physical link interference. Our result thus bridges the gap between static graph-based interference models and the physical SINR model. Based on these results, we also show that when it comes to scheduling, requiring the communication links to be symmetric may imply significantly higher costs as opposed to topologies allowing unidirectional links. Many topology-dependent transmission scheduling algorithms have been proposed to minimize the time-division multiple-access frame length in multihop packet radio networks (MPRNs), in which changes of the topology inevitably require recomputation of the schedules. The need for constant adaptation of schedules-to-mobile topology entails significant problems, especially in highly dynamic mobile environments. Hence, topology-transparent scheduling algorithms have been proposed, which utilize Galois field theory and Latin squares theory. We discuss the topology-transparent broadcast scheduling design for MPRNs. For single-channel networks, we propose the modified Galois field design (MGD) and the Latin square design (LSD) for topology-transparent broadcast scheduling. The MGD obtains much smaller minimum frame length (MFL) than the existing scheme while the LSD can even achieve possible performance gain when compared with the MGD, under certain conditions. Moreover, the inner relationship between scheduling designs based on different theories is revealed and proved, which provides valuable insight. For topology-transparent broadcast scheduling in multichannel networks, in which little research has been done, the proposed multichannel Galois field design (MCGD) can reduce the MFL approximately M times, as compared with the MGD when M channels are available. Numerical results show that the proposed algorithms outperform existing algorithms in achieving a smaller MFL. The steadily increasing number of nodes in high-performance computing systems and the technology and power constraints lead to sparse network topologies. Efficient mapping of application communication patterns to the network topology gains importance as systems grow to petascale and beyond. Such mapping is supported in parallel programming frameworks such as MPI, but is often not well implemented. We show that the topology mapping problem is NP-complete and analyze and compare different practical topology mapping heuristics. We demonstrate an efficient and fast new heuristic which is based on graph similarity and show its utility with application communication patterns on real topologies. Our mapping strategies support heterogeneous networks and show significant reduction of congestion on torus, fat-tree, and the PERCS network topologies, for irregular communication patterns. We also demonstrate that the benefit of topology mapping grows with the network size and show how our algorithms can be used in a practical setting to optimize communication performance. Our efficient topology mapping strategies are shown to reduce network congestion by up to 80 , reduce average dilation by up to 50 , and improve benchmarked communication performance by 18 .