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This paper focuses on the problem of finding multiple paths with relay nodes to maximize throughput for ultra-high-rate millimeter wave (mmWave) backhaul networks in urban environments. Relays are selected between a pair of source and destination base stations to form multiple interference-free paths. We first formulate the problem of feasibility of multi-path construction as a constraint satisfaction problem that includes constraints on intra-path and inter-path interference and several other constraints that arise from the problem setting. Based on the derived equations, we transform the multiple paths construction problem into a Boolean satisfiability problem. This problem can then be solved through use of a satisfiability (SAT) solver, which however results in a very high running time for realistic problem sizes. To address this, we propose a heuristic algorithm that runs in a fraction of the time of the SAT solver and finds multiple interference-free paths using a modification of a maximum flow algorithm. Simulation results based on 3-D models of a section of downtown Atlanta show that the heuristic algorithm finds multiple paths in almost all the feasible cases (those where the SAT solver succeeds in finding a solution) and produces paths with higher average throughput than the SAT solver. Furthermore, the heuristic increases throughput by 50-100% in typical cases compared to a single-path solution.
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A Theory of Alternating Paths and Blossoms from the Perspective of Minimum Length
The Micali–Vazirani (MV) algorithm for finding a maximum cardinality matching in general graphs, which was published in 1980, remains to this day the most efficient known algorithm for the problem. The current paper gives the first complete and correct proof of this algorithm. The MV algorithm resorts to finding minimum-length augmenting paths. However, such paths fail to satisfy an elementary property, called breadth first search honesty in this paper. In the absence of this property, an exponential time algorithm appears to be called for—just for finding one such path. On the other hand, the MV algorithm accomplishes this and additional tasks in linear time. The saving grace is the various “footholds” offered by the underlying structure, which the algorithm uses in order to perform its key tasks efficiently. The theory expounded in this paper elucidates this rich structure and yields a proof of correctness of the algorithm. It may also be of independent interest as a set of well-knit graph-theoretic facts.
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- Award ID(s):
- 2230414
- PAR ID:
- 10627966
- Publisher / Repository:
- Informs
- Date Published:
- Journal Name:
- Mathematics of operations research
- ISSN:
- 0364-765X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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