OFDP算法：无线传感器网络中最小能耗的不相交路径发现
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更新于2024-07-15
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OFDP（Optimally-Finding-Disjoint-Paths）是一种针对无线传感器网络设计的分布式算法，其主要目标是在给定的网络环境中寻找两个节点s和t之间k条互不相交的最短路径，从而最小化总路径长度。这是一项具有挑战性的优化问题，被称为Minimum-length-k-Disjoint-Paths (MIN-k-DP)问题。
在无线传感器网络中，节点通常受限于能源和通信能力，因此算法的设计不仅要考虑路径的连接性，还要注重能量效率。OFDP算法通过分布式的方式处理这个任务，避免了集中式解决方案可能面临的通信负担和节点资源消耗。它的核心优势在于：
1. **正确性和最优性保证**：OFDP算法确保如果网络中有k条互不相交的路径，它一定能找到这k条路径；即使在网络中无法找到k条这样的路径，它也能找到尽可能多且总长度最短的路径。这种双重保证使得OFDP在解决MIN-k-DP问题时表现出高度的可靠性。
2. **与现有算法比较**：与那些同样提供正确性和最优性保证的中央集权算法相比，OFDP在实际应用中的效率更高。由于分布式特性，OFDP减少了通信需求和数据集中处理的时间，这意味着它在大规模或复杂网络结构中具有明显的优势，尤其是在资源受限的无线环境里。
3. **研究成果**：该论文发表在《组合优化》(JCombOptim)上，引用号为DOI:10.1007/s10878-015-9845-2，作者包括Kejia Zhang、Qilong Han、Guisheng Yin和Haiwei Pan。他们的工作填补了分布式算法领域的一个空白，为无线传感器网络中的路径规划提供了一种高效且性能优越的新方法。
OFDP算法在无线传感器网络中寻找最少能耗的不相交路径问题上具有重要意义，不仅解决了实际问题，而且在算法设计上实现了性能与效率的平衡，对于未来此类网络的优化管理和能耗管理具有潜在的实用价值。
J Comb Optim
total length in the given network as shown in Fig. 1b. Using these algorithms, we will
find the first path P
1
= (s, a, b, c, t) and the second path P
2
= (s, d, e, h, t) as shown
by bold lines in Fig. 1b. The total length of P
1
and P
2
is 4 + 13 = 17. However, the
optimal answer should be P
1
= (s, d, e, c, t) and P
2
= (s, a, f, g, t) with total length
6 + 6 = 12.
We propose a distributed algorithm in Zhang et al. (2014) to find k disjoint s ∼ t
paths with correctness guarantee. However, the algorithm does not consider the length
of the routing paths.
In Srinivas and Modiano (2003), Bhandari (1997), Khuller and Schieber (1989),
Iwama et al. (1997), Suurballe (1974), Chen et al. (2004), and Hashiguchi et al. ( 2011),
some centralized algorithms are given for finding k disjoint s ∼ t paths in graphs.
All these algorithm guarantee correctness. In particular, the algorithms in Srinivas
and Modiano (2003), Bhandari (1997), Suurballe (1974), and Hashiguchi et al. (2011)
will find k disjoint s ∼ t paths with the minimum total length, i.e., they guarantee
both correctness and optimality. If we use these centralized algorithms to solve the
MIN-k-DP problem in a WSN, we have to collect every node’s neighbor list to build
the topology of the whole network. The communication cost of such operation is very
high for a large-scale network.
The works in Bley (2003),
Itai et al. (1982), and Ronen and Perl (1984) consider the
problem of finding the maximum number of length-bounded disjoint s ∼ t paths in
graphs. A length-bounded path is a path whose length is no more than a user-specified
threshold l.InItai et al. (1982), this problem is proven to be NP-Hard for l ≥ 5. In Bley
(2003), this problem is further proven to be APX-Complete for l ≥ 5, which means
that there is no Polynomial Time Approximation Scheme (PTAS) for this problem.
A heuristic algorithm for this problem is given in Ronen and Perl (1984) without
approximation bound.
So far, all the existing algorithms which can solve the MIN-k-DP problem with
correctness and optimality guarantee are centralized algorithms. These centralized
algorithms need to build the topology of the whole network, which makes them not
applicable in WSNs. On the other hand, all the distributed algorithms can not guarantee
correctness or optimality. Therefore, we have two challenges to solve the MIN-k-
DP problem in WSNs: (1) to guarantee correctness and optimality, (2) to maintain
efficiency.
3 Preliminaries
The given sensor network can be expressed as a weighted undirected graph G =
(V, E), where V ={v | v is a sensor node }, E ={(u,v) | there is a wireless link
between u ∈ V and v ∈ V }. Function l : E → R
+
defines the lengths of the edges in
E, which denotes the energy cost or transmission delay of the corresponding links. We
assume that all the links are bidirectional, i.e., u can hear v if v can hear u. Hereinafter,
we do not distinguish the terms “network” and “graph”. For simplicity, we use l(u,v)
rather than l((u,v))to denote the length of edge (u,v).
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