Solving Steiner trees: Recent advances, challenges, and perspectives

Ljubić, Ivana

doi:10.1002/net.22005

Cited by 41 publications

(18 citation statements)

References 214 publications

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“…See [49,17] for surveys, where they refer it as the profitable tour problem and [44] for a particularly relevant example. See also [32,28] for exact branch-and-cut and dual ascent-based branch-andbound methods for the closely-related net-worth maximizing Steiner tree problem, respectively, and [31] for a survey on recent developments. We emphasize that, for this particular problem, these methods take exponential time in the worst case.…”

Section: Dual Separationmentioning

confidence: 99%

On the Request-Trip-Vehicle Assignment Problem

Mori¹,

Samaranayake²

2021

SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)

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The request-trip-vehicle assignment problem is at the heart of a popular decomposition strategy for online vehicle routing. In this framework, assignments are done in batches in order to exploit any shareability among vehicles and incoming travel requests. We study a natural ILP formulation and its LP relaxation. Our main result is an LP-based randomized rounding algorithm that, whenever the instance is feasible, leverages mild assumptions to return an assignment whose: i) expected cost is at most that of an optimal solution, and ii) expected fraction of unassigned requests is at most 1/e. If trip-vehicle assignment costs are α-approximate, we pay an additional factor of α in the expected cost. We can relax the feasibility requirement by considering the penalty version of the problem, in which a penalty is paid for each unassigned request. We find that, whenever a request is repeatedly unassigned after a number of rounds, with high probability it is so in accordance with the sequence of LP solutions and not because of a rounding error. We additionally introduce a deterministic rounding heuristic inspired by our randomized technique. Our computational experiments show that our rounding algorithms achieve a performance similar to that of the ILP at a reduced computation time, far improving on our theoretical guarantee. The reason for this is that, although the assignment problem is hard in theory, the natural LP relaxation tends to be very tight in practice.

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Section: Dual Separationmentioning

confidence: 99%

On the Request-Trip-Vehicle Assignment Problem

Mori¹,

Samaranayake²

2021

SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)

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“…Many references where multicast routing is tackled by using a Steiner tree approach are cited in [2]. Here we emphasize some contributions in this topic, in particular regarding the BRSMT problem which is more common.…”

Section: Related Workmentioning

confidence: 99%

“…Constraints ( 3) and ( 4) guarantee the correct assignment of variables y ij , that account for the links belonging to the Steiner tree, by making use of variables x tk ij : constraints (3) guarantee that each path defined in (2) can only transverse links belonging to the Steiner tree, whereas constraints (4) guarantee that a link belongs to the Steiner tree if it belongs to one of the paths defined in (2).…”

Section: Ilp Model For the Stp With Delay Constraintsmentioning

confidence: 99%

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Determining the Minimum Cost Steiner Tree for Delay Constrained Problems

et al. 2021

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“…Networks has published a large number of articles on the Steiner tree problem, including two surveys, one each in 1987 and 1992. Ljubić [5] starts off this issue with a comprehensive overview of the rich developments on the Steiner tree problem over the last three decades. The paper highlights advances in tools and techniques, with a greater focus on computational advances.…”

mentioning

confidence: 99%