Approximation Algorithms for Car-Sharing Problems

Luo, Kelin; Spieksma, Frits

doi:10.1007/978-3-030-58150-3_21

Cited by 7 publications

(7 citation statements)

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“…We also define an algorithm, the CA, that consists of outputting the better of the solutions found by the TA and MA. An overview of the results for c = 2 is shown in Table 2 (see also [22]). Notice that for CS sum,s=t , CS lat , and CS lat,s=t , the worst-case ratio of the combined algorithm (CA) is strictly better than each of the two worst-case ratios of the individual algorithms f which CA is composed.…”

Section: Our Resultsmentioning

confidence: 99%

“…Bei and Zhang [9] considered CS sum with c = 2 and gave a 2.5-approximation algorithm for it. Luo and Spieksma [22] proposed approximation algorithms for four versions of the problem, while still assuming c = 2. Here, we generalize the ride-sharing problem to a problem involving any arbitrary constant c ≥ 2.…”

Section: Related Workmentioning

confidence: 99%

“…In this section, we consider the ride-sharing problems CS sum , CS sum,s=t , CS lat , and CS lat,s=t with capacity c = 2 and each car serving exactly two requests, i.e., m = 2n (see [22]). In Section 4.1, we propose and analyze the match-and-assign algorithm (MA).…”

Section: The Case C = 2: Algorithms and Their Analysismentioning

confidence: 99%

“…If two points are not connected by an edge, their travel time equals five. Observe that an optimal solution is {(k 1 , {1, 3}), (k 2 , {2, 4})} with wait(M * (I)) = Based on the µ values as defined in (22), the MA(2, µ) can find, in the first step, matching…”

Section: : Matching Stepmentioning

confidence: 99%

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Minimizing Travel Time and Latency in Multi-Capacity Ride-Sharing Problems

Luo

Spieksma

2022

Algorithms

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Motivated by applications in ride-sharing and truck-delivery, we study the problem of matching a number of requests and assigning them to cars. A number of cars are given, each of which consists of a location and a speed, and a number of requests are given, each of which consists of a pick-up location and a drop-off location. Serving a request means that a car must first visit the pick-up location of the request and then visit the drop-off location. Each car can only serve at most c requests. Each assignment can yield multiple different serving routes and corresponding serving times, and our goal was to serve the maximum number of requests with the minimum travel time (called CSsum) and to serve the maximum number of requests with the minimum total latency (called CSlat). In addition, we studied the special case where the pick-up and drop-off locations of a request coincide. Both problems CSsum and CSlat are APX-hard when c≥2. We propose an algorithm, called the transportation algorithm (TA), which is a (2c−1)-approximation (resp. c-approximation) algorithm for CSsum (resp. CSlat); these bounds are shown to be tight. We also considered the special case where each car serves exactly two requests, i.e., c=2. In addition to the TA, we investigated another algorithm, called the match-and-assign algorithm (MA). Moreover, we call the algorithm that outputs the best of the two solutions found by the TA and MA the CA. We show that the CA is a two-approximation (resp. 5/3) for CSsum (resp. CSlat), and these ratios are better than the ratios of the individual algorithms, the TA and MA.

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Section: Our Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: The Case C = 2: Algorithms and Their Analysismentioning

confidence: 99%

Section: : Matching Stepmentioning

confidence: 99%

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Minimizing Travel Time and Latency in Multi-Capacity Ride-Sharing Problems

Luo

Spieksma

2022

Algorithms

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“…Namely, they only require there being at most twice as many requests as there are vehicles. Luo and Spieksma [35] obtain a 2-approximation algorithm under the same assumptions as in [6]. They also obtain a 5/3-approximation when the objective is to minimize the total latency.…”

Section: Introductionmentioning

confidence: 96%

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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