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Best upgrade plans for single and multiple source-destination pairs

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Abstract

In this paper, we study Resource Constrained Best Upgrade Plan (BUP) computation in road network databases. Consider a transportation network (weighted graph) G where a subset of the edges are upgradable, i.e., for each such edge there is a cost, which if spent, the weight of the edge can be reduced to a specific new value. In the single-pair version of BUP, the input includes a source and a destination in G, and a budget B (resource constraint). The goal is to identify which upgradable edges should be upgraded so that the shortest path distance between source and destination (in the updated network) is minimized, without exceeding the available budget for the upgrade. In the multiple-pair version of BUP, a set Q of source-destination pairs is given, and the problem is to choose for upgrade those edges that lead to the smallest sum of shortest path distances across all pairs in Q, subject to budget constraint B. In addition to transportation networks, the BUP query arises in other domains too, such as telecommunications. We propose a framework for BUP processing and evaluate it with experiments on large, real road networks.

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Notes

  1. In case of tie between two alternative paths, we keep as p ∗ the one with the smallest C(R p*).

  2. Note that in A(G c ) it is unambiguous whether the path passes via an upgraded or un-upgraded link between two nodes – similarly, it is clear how to measure the upgrade cost.

    Table 2 Ranked paths for the two source-destination pairs in running example
    Full size table

  3. Note that here SP is an umbrella concept covering any path that passes via the same nodes as SP, regardless of which edges are chosen for upgrade.

  4. Note that Lemma 7 uses U c instead of U because it is applied on G c (not on G).

  5. For completeness, we mention that a brute force evaluation of subsets of U c (after “Pruning+Preserver” reduction) in our default setting for single-pair BUP takes longer than 20sec, which is orders of magnitude slower than our methods, evaluated shortly.

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  1. School of Information Systems, Singapore Management University, 80 Stamford Road, Singapore, 178902, Singapore

    Yimin Lin & Kyriakos Mouratidis

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  1. Yimin Lin
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  2. Kyriakos Mouratidis
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Correspondence to Kyriakos Mouratidis.

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Lin, Y., Mouratidis, K. Best upgrade plans for single and multiple source-destination pairs. Geoinformatica 19, 365–404 (2015). https://doi.org/10.1007/s10707-014-0219-1

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