The Fast Heuristic Algorithms and Post-Processing Techniques to Design Large and Low-Cost Communication Networks

Sun, Yahui; Brazil, Marcus; Thomas, Doreen A.; Halgamuge, Saman K.

doi:10.1109/tnet.2018.2888864

Cited by 11 publications

(3 citation statements)

References 34 publications

(51 reference statements)

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“…Early work focused on approximation schemes (e.g., Goemans and Williamson, 1995;Johnson et al, 2000). Fast heuristics have application in some settings and a recent example is given in Sun et al (2019). However, for the purposes of solving the concatenation subproblem for PCEST, an exact solution to PCSTG is ideal.…”

Section: Pcstg Problemmentioning

confidence: 99%

Solving the prize‐collecting Euclidean Steiner tree problem

Whittle

Brazil

Grossman

et al. 2020

Int Trans Operational Res

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The prize-collecting Euclidean Steiner tree (PCEST) problem is a generalization of the well-known Euclidean Steiner tree (EST) problem. All points given in an EST problem instance are connected by the shortest possible network in a solution. A solution can include additional points called Steiner points. A PCEST problem instance differs from an EST problem instance by the addition of weights for each given point. A PCEST solution connects a subset of the given points in order to maximize the net value of the network (the sum of the selected point weights, less than the length of the network). We present an algorithmic framework for solving the PCEST problem. Included in the framework are efficient methods to determine subsets of points that must be in every solution, and subsets of points that cannot be in any solution. Also included are methods to generate and concatenate full Steiner trees.

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Section: Pcstg Problemmentioning

confidence: 99%

Solving the prize‐collecting Euclidean Steiner tree problem

Whittle

Brazil

Grossman

et al. 2020

Int Trans Operational Res

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“…1 shows an example. Gilbert and Pollack [2] are often credited for formalising the Steiner minimal tree problem which has direct applications to VLSI design [4], [5], communication network optimization [6], [7], computational and systems biology [8], [9], and knowledge discovery and management [10], [11]. The problem of finding a Steiner minimal tree of a graph and arbitrary seed vertices is known to be NP-hard (the decision variant is NP-complete) [1], [12].…”

Section: Introductionmentioning

confidence: 99%

Towards Distributed 2-Approximation Steiner Minimal Trees in Billion-edge Graphs

Reza¹,

Sanders²,

Pearce³

2022

Preprint

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Given an edge-weighted graph and a set of known seed vertices of interest, a network scientist often desires to understand the graph relationships to explain connections between the seed vertices. If the size of the seed set is 2, shortest path calculations are an attractive computational kernel to explore the connections between the two vertices. When the seed set is 3 or larger (say up to 1,000s) Steiner minimal tree -min-weight acyclic connected subgraph (of the input graph) that contains all the seed vertices -is an attractive generalization of shortest weighted paths. In general, computing a Steiner minimal tree is NP-hard, but decades ago several polynomial-time algorithms were designed and proven to yield Steiner trees whose total weight is bounded within 2 times the minimal Steiner tree.Despite its rich theoretical literature, works related to parallel Steiner minimal tree computation and their scalable implementations are rather scarce. In this paper, we present a parallel 2approximation Steiner minimal tree algorithm (with theoretical guarantees) and its MPI-based distributed implementation. In place of distance computation between all pairs of seed vertices, an expensive phase in many approximation algorithms, the solution we employ, exploits Voronoi cell computation. Also, this approach has higher parallel efficiency than others that involve minimum spanning tree computation on the entire graph. Furthermore, our distributed design exploits asynchronous processing and a message prioritization scheme to accelerate convergence of distance computation, employs techniques to avoid inefficient distributed spanning tree computation on the entire graph, and harnesses a combination of vertex and edge centric processing to offer fast time-to-solution. We demonstrate scalability and performance of our solution using real-world graphs with up to 128 billion edges and 512 compute nodes (8K processes), show the ability to find Steiner trees with up to 10K seed vertices in under one minute, and present in-depth analyses that highlight the benefits of our design choices. Using four real-world graphs and three seed sets for each, we compare our solution with the state-of-the-art exact Steiner minimal tree solver, SCIP-Jack, and two sequential algorithms with the same approximation bound as our algorithm. Our distributed solution comfortably outperforms these related works on graphs with 10s million edges and offers decent strong scaling -up to 90% efficient. We empirically show that, on average, the total distance (sum of edge weights) of the Steiner tree identified by our solution is 1.0527 times greater than the Steiner minimal tree (i.e., the optimal solution) -well within the theoretical bound of less than equal to 2.

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“…[18]), while heuristic and post-processing algorithms are often combined together to produce fast suboptimal solutions for large instances (e.g. [19]), where heuristic algorithms produce fast suboptimal solutions and post-processing algorithms improve these solutions. In this paper, we will develop all these types of algorithms for our application.…”

Section: Introductionmentioning

confidence: 99%

Minimum-Cost Heterogeneous Node Placement in Wireless Sensor Networks

Sun

Halgamuge

2019

IEEE Access

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The operational cost-effectiveness of wireless sensor networks depends on the placement of heterogeneous nodes: base stations, sensor nodes, and relay nodes. To achieve the global optimality of minimum-cost heterogeneous node placement, we find the locations of base stations, sensor nodes, and relay nodes, simultaneously. The objective is to minimize the sum of node production and placement costs and transmission outage probabilities in the routing tree. First, we formulate this minimum-cost heterogeneous node placement problem as a new NP-hard Steiner tree problem. Then, to solve this problem for both small and large instances, we propose an exponential-time exact algorithm, a polynomial-time heuristic algorithm, and several post-processing algorithms. On a personal computer, our exact algorithm is sufficiently fast to produce optimal solutions for small instances with dozens of vertices, while our heuristic and postprocessing algorithms can, respectively, produce and improve suboptimal solutions for large instances with 100 000 vertices and 1 000 000 edges within 6 s. We also compare the heuristic and optimal solutions for small instances with dozens of vertices and show that the ratios between the respective solution costs are generally below 1.35, and our post-processing algorithms can improve this number to 1.1. This indicates that our heuristic and post-processing algorithms are likely to produce near-optimal solutions in practice and are useful for minimum-cost heterogeneous node placement when computational resources are scarce. INDEX TERMS Steiner tree problem, wireless sensor network, Internet of Things.

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The Fast Heuristic Algorithms and Post-Processing Techniques to Design Large and Low-Cost Communication Networks

Cited by 11 publications

References 34 publications

Solving the prize‐collecting Euclidean Steiner tree problem

Solving the prize‐collecting Euclidean Steiner tree problem

Towards Distributed 2-Approximation Steiner Minimal Trees in Billion-edge Graphs

Minimum-Cost Heterogeneous Node Placement in Wireless Sensor Networks

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