The Covering Canadian Traveller Problem Revisited

In this paper, we consider the k-Covering Canadian Traveller Problem (k-CCTP), which can be seen as a variant of the Travelling Salesperson Problem. The goal of k-CCTP is finding the shortest tour for a traveller to visit a set of locations in a given graph and return to the origin. Crucially, unknown to the traveller, up to k edges of the graph are blocked and the traveller only discovers blocked edges online at one of their respective endpoints. The currently best known upper bound for k-CCTP is O(?k) which was shown in [Huang and Liao, ISAAC \u2712]. We improve this polynomial bound to a logarithmic one by presenting a deterministic O(log k)-competitive algorithm that runs in polynomial time. Further, we demonstrate the tightness of our analysis by giving a lower bound instance for our algorithm

Canadian Traveller Problem with Predictions

In this work, we consider the $k$-Canadian Traveller Problem ($k$-CTP) under the learning-augmented framework proposed by Lykouris & Vassilvitskii. $k$-CTP is a generalization of the shortest path problem, and involves a traveller who knows the entire graph in advance and wishes to find the shortest route from a source vertex $s$ to a destination vertex $t$, but discovers online that some edges (up to $k$) are blocked once reaching them. A potentially imperfect predictor gives us the number and the locations of the blocked edges. We present a deterministic and a randomized online algorithm for the learning-augmented $k$-CTP that achieve a tradeoff between consistency (quality of the solution when the prediction is correct) and robustness (quality of the solution when there are errors in the prediction). Moreover, we prove a matching lower bound for the deterministic case establishing that the tradeoff between consistency and robustness is optimal, and show a lower bound for the randomized algorithm. Finally, we prove several deterministic and randomized lower bounds on the competitive ratio of $k$-CTP depending on the prediction error, and complement them, in most cases, with matching upper bounds

Canadians Should Travel Randomly

We study online algorithms for the Canadian Traveller Problem (CTP) introduced by Papadimitriou and Yannakakis in 1991. In this problem, a traveller knows the entire road network in advance, and wishes to travel as quickly as possible from a source vertex s to a destination vertex t, but discovers online that some roads are blocked (e.g., by snow) once reaching them. It is PSPACE-complete to achieve a bounded competitive ratio for this problem. Furthermore, if at most k roads can be blocked, then the optimal competitive ratio for a deterministic online algorithm is 2k + 1, while the only randomized result known is a lower bound of k + 1. In this paper, we show for the first time that a polynomial time randomized algorithm can beat the best deterministic algorithms, surpassing the 2k + 1 lower bound by an o(1) factor. Moreover, we prove the randomized algorithm achieving a competitive ratio of (1 + [√2 over 2])k + 1 in pseudo-polynomial time. The proposed techniques can also be applied to implicitly represent multiple near-shortest s-t paths.NSC Grant 102-2221-E-007-075-MY3Japan Society for the Promotion of Science (KAKENHI 23240002

Exact Algorithms for the Canadian Traveller Problem on Paths and Trees

The Canadian Traveller problem is a stochastic shortest paths problem in which one learns the cost of an edge only when arriving at one of its endpoints. The goal is to find an adaptive policy (adjusting as one learns more edge lengths) that minimizes the expected cost of travel. The problem is known to be #P hard. Since there has been no significant progress on approximation algorithms for several decades, we have chosen to seek out special cases for which exact solutions exist, in the hope of demonstrating techniques that could lead to further progress. Applying techniques from the theory of Markov Decision Processes, we give an exact solution for graphs of parallel (undirected) paths from source to destination with random two-valued edge costs. We also offer a partial generalization to traversing perfect binary trees

Efficient Routing for Disaster Scenarios in Uncertain Networks: A Computational Study of Adaptive Algorithms for the Stochastic Canadian Traveler Problem with Multiple Agents and Destinations

The primary objective of this research is to develop adaptive online algorithms for solving the Canadian Traveler Problem (CTP), which is a well-studied problem in the literature that has important applications in disaster scenarios. To this end, we propose two novel approaches, namely Maximum Likely Node (MLN) and Maximum Likely Path (MLP), to address the single-agent single-destination variant of the CTP. Our computational experiments demonstrate that the MLN and MLP algorithms together achieve new best-known solutions for 10,715 instances. In the context of disaster scenarios, the CTP can be extended to the multiple-agent multiple-destination variant, which we refer to as MAD-CTP. We propose two approaches, namely MAD-OMT and MAD-HOP, to solve this variant. We evaluate the performance of these algorithms on Delaunay and Euclidean graphs of varying sizes, ranging from 20 nodes with 49 edges to 500 nodes with 1500 edges. Our results demonstrate that MAD-HOP outperforms MAD-OMT by a considerable margin, achieving a replan time of under 9 seconds for all instances. Furthermore, we extend the existing state-of-the-art algorithm, UCT, which was previously shown by Eyerich et al. (2010) to be effective for solving the single-source single-destination variant of the CTP, to address the MAD-CTP problem. We compare the performance of UCT and MAD-HOP on a range of instances, and our results indicate that MAD-HOP offers better performance than UCT on most instances. In addition, UCT exhibited a very high replan time of around 10 minutes. The inferior results of UCT may be attributed to the number of rollouts used in the experiments but increasing the number of rollouts did not conclusively demonstrate whether UCT could outperform MAD-HOP. This may be due to the benefits obtained from using multiple agents, as MAD-HOP appears to benefit to a greater extent than UCT when information is shared among agents

Efficient Routing for Disaster Scenarios in Uncertain Networks: A Computational Study of Adaptive Algorithms for the Stochastic Canadian Traveler Problem with Multiple Agents and Destinations

The primary objective of this research is to develop adaptive online algorithms for solving the Canadian Traveler Problem (CTP), which is a well-studied problem in the literature that has important applications in disaster scenarios. To this end, we propose two novel approaches, namely Maximum Likely Node (MLN) and Maximum Likely Path (MLP), to address the single-agent single-destination variant of the CTP. Our computational experiments demonstrate that the MLN and MLP algorithms together achieve new best-known solutions for 10,715 instances. In the context of disaster scenarios, the CTP can be extended to the multiple-agent multiple-destination variant, which we refer to as MAD-CTP. We propose two approaches, namely MAD-OMT and MAD-HOP, to solve this variant. We evaluate the performance of these algorithms on Delaunay and Euclidean graphs of varying sizes, ranging from 20 nodes with 49 edges to 500 nodes with 1500 edges. Our results demonstrate that MAD-HOP outperforms MAD-OMT by a considerable margin, achieving a replan time of under 9 seconds for all instances. Furthermore, we extend the existing state-of-the-art algorithm, UCT, which was previously shown by Eyerich et al. (2010) to be effective for solving the single-source single-destination variant of the CTP, to address the MAD-CTP problem. We compare the performance of UCT and MAD-HOP on a range of instances, and our results indicate that MAD-HOP offers better performance than UCT on most instances. In addition, UCT exhibited a very high replan time of around 10 minutes. The inferior results of UCT may be attributed to the number of rollouts used in the experiments but increasing the number of rollouts did not conclusively demonstrate whether UCT could outperform MAD-HOP. This may be due to the benefits obtained from using multiple agents, as MAD-HOP appears to benefit to a greater extent than UCT when information is shared among agents

Connecting Cultures

Publisher PD

\u3ci\u3eThe Conference Proceedings of the 1998 Air Transport Research Group (ATRG) of the WCTR Society, Volume 3 \u3c/i\u3e

UNOAI Report 98-8https://digitalcommons.unomaha.edu/facultybooks/1151/thumbnail.jp

Solving Spectrum Gridlock: Reforms to Liberalize Radio Spectrum Management in Canada in the Face of Growing Scarcity

Canada lags other countries in solving the problem of spectrum scarcity amid rising demand driven by cellphones and other wireless products. In this study, the authors call for reforms to liberalize the allocation of spectrum in Canada with a market-based approach, to increase competition, for the benefit of consumers and other end users.Economic Growth and Innovation, radio spectrum, wireless technology, Industry Canada