Heat-Diffusion (HD) routing is our recently-developed queue-aware routing policy for multi-hop wireless networks inspired by Thermodynamics. In the prior theoretical studies, we have shown that HD routing guarantees throughput optimality, minimizes a quadratic routing cost, minimizes queue congestion on the network, and provides a trade-off between routing cost and queueing delay that is Pareto-Optimal. While striking, these guarantees are based on idealized assumptions (including global synchronization, centralized control, and infinite buffers) and heretofore have only been evaluated through simplified numerical simulations. We present here the first practical decentralized Heat-Diffusion Collection Protocol (HDCP) for wireless sensor networks and detail its implementation on Contiki OS. We present a thorough evaluation of HDCP based on real testbed experiments, including a comparative analysis of its performance with respect to the state of the art Collection Tree Protocol (CTP) and Backpressure Collection Protocol (BCP) for wireless sensor networks. We find that HDCP has a significantly higher throughput region and greater resilience to interference compared to CTP. However, we also find that the best performance of HDCP is comparable to the best performance of BCP, due to the similarity in their neighbor rankings, which we verify through a Kendall's-Tau test.
In our prior works, we have presented the idealized Heat Diffusion routing algorithm @cite_20 @cite_1 . All of these are network theory papers that spell out a centralized algorithm, assume global synchronization, assume that at each time step a NP-hard Maximum Weight Independent Set problem can be solved, and that all queues are of unlimited size, and under these assumptions prove various properties of the HD algorithm. The only evaluations presented in these works are idealized MATLAB simulations. This work is clearly inspired by and built up on our earlier works on HD routing, but is the first to develop and implement it as a realistic distributed protocol (HDCP) and evaluate it on a real testbed.
@cite_1 @cite_20
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In this paper, we introduce a distributed dynamic routing algorithm in multi-hop cognitive radio (CR) networks, in which secondary users (SUs) want to minimize their interference to the primary users (PUs) while keeping the delay along the route low. We employ a cognitive pilot channel (CPC) for SUs to be able to access the information about PUs, including PUs' locations and channel conditions. Medial axis with a relaxation factor is used as a reference path for the routing, along which we develop a hierarchical structure for multiple sources to reach their destinations. We introduce a temporal and spatial dynamic non-cooperative game to model the interactions among the SUs as well as their influences on the PUs, and obtain by backward induction a set of mixed (behavioral) Nash equilibrium strategies. We also employ a multi-stage fictitious play learning algorithm for distributed routing, which minimizes the overall interference from the SUs to the PUs, as well as the average packet delay along the route from the SU nodes to their destinations. Simulation results show that our proposed algorithm can avoid congestion in the CR network and minimize delay while keeping the interference level low. We describe a distributed randomized algorithm to construct routing tables. Given 0< e <= 1 2, the algorithm runs in time O(n1 2+e + HD), where n is the number of nodes and HD denotes the diameter of the network in hops (i.e., as if the network is unweighted). The weighted length of the produced routes is at most O(e-1log e-1) times the optimal weighted length. This is the first algorithm to break the Omega(n) complexity barrier for computing weighted shortest paths even for a single source. Moreover, the algorithm nearly meets the Omega(n1 2 + HD) lower bound for distributed computation of routing tables and approximate distances (with optimality, up to polylog factors, for e=1 log n). The presented techniques have many applications, including improved distributed approximation algorithms for Generalized Steiner Forest, all-pairs distance estimation, and estimation of the weighted diameter. This paper considers max-min fair rate allocation and routing in energy harvesting networks where fairness is required among both the nodes and the time slots. Unlike most previous work on fairness, we focus on multihop topologies and consider different routing methods. We assume a predictable energy profile and focus on the design of efficient and optimal algorithms that can serve as benchmarks for distributed and approximate algorithms. We first develop an algorithm that obtains a max-min fair rate assignment for any given (time-variable or time-invariable) unsplittable routing or a routing tree. For time-invariable unsplittable routing, we also develop an algorithm that finds routes that maximize the minimum rate assigned to any node in any slot. For fractional routing, we study the joint routing and rate assignment problem. We develop an algorithm for the time-invariable case with constant rates. We show that the time-variable case is at least as hard as the 2-commodity feasible flow problem and design an FPTAS to combat the high running time. Finally, we show that finding a max-min fair unsplittable routing or a routing tree is NP-hard, even for a time horizon of a single slot. Our analysis provides insights into the problem structure and can be applied to other related fairness problems. We study approximate distributed solutions to the weighted all-pairs shortest-paths (APSP) problem in the CONGEST model. We obtain the following results. A deterministic (1+epsilon)-approximation to APSP with running time O(e-2n log n) rounds. The best previously known algorithm was randomized and slower by a Theta(log n) factor. In many cases, routing schemes involve relabeling, i.e., assigning new names to nodes and that are used in distance and routing queries. It is known that relabeling is necessary to achieve running times of o(n log n). In the relabeling model, we obtain the following results. A randomized O(k)-approximation to APSP, for any integer k>1, running in O(n1 2+1 k+D) rounds, where D is the hop diameter of the network. This algorithm simplifies the best previously known result and reduces its approximation ratio from O(k log k) to O(k). Also, the new algorithm uses O(log n)-bit labels, which is asymptotically optimal. A randomized O(k)-approximation to APSP, for any integer k>1, running in time O((nD)1 2 n1 k+D) and producing compact routing tables of size O(n1 k). The node labels consist of O(k log n) bits. This improves on the approximation ratio of Theta(k2) for tables of that size achieved by the best previously known algorithm, which terminates faster, in O(n1 2+1 k+D) rounds. In addition, we improve on the time complexity of the best known deterministic algorithm for distributed approximate Steiner forest.