17,789 research outputs found
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
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
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
Canadian Traveller Problem with Predictions
In this work, we consider the -Canadian Traveller Problem (-CTP) under
the learning-augmented framework proposed by Lykouris & Vassilvitskii. -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 to a destination vertex , but discovers online that some
edges (up to ) 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 -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 -CTP depending on the prediction
error, and complement them, in most cases, with matching upper bounds
Tour-based Travel Mode Choice Estimation based on Data Mining and Fuzzy Techniques
This paper extends tour-based mode choice model, which mainly includes individual trip level interactions, to include
linked travel modes of consecutive trips of an individual. Travel modes of consecutive trip made by an individual in a
household have strong dependency or co-relation because individuals try to maintain their travel modes or use a few
combinations of modes for current and subsequent trips. Traditionally, tour based mode choice models involved nested
logit models derived from expert knowledge. There are limitations associated with this approach. Logit models assumes
i) specific model structure (linear utility model) in advance; and, ii) it holds across an entire historical observations.
These assumptions about the predefined model may be representative of reality, however these rules or heuristics
for tour based mode choice should ideally be derived from the survey data rather than based on expert knowledge/
judgment. Therefore, in this paper, we propose a novel data-driven methodology to address the issues identified in tour
based mode choice. The proposed methodology is tested using the Household Travel Survey (HTS) data of Sydney
metropolitan area and its performances are compared with the state-of-the-art approaches in this area
Traversable Wormholes in (2+1) and (3+1) Dimensions with a Cosmological Constant
Macroscopic traversable wormhole solutions to Einstein's field equations in
and dimensions with a cosmological constant are investigated.
Ensuring traversability severely constrains the material used to generate the
wormhole's spacetime curvature. Although the presence of a cosmological
constant modifies to some extent the type of matter permitted (for example it
is possible to have a positive energy density for the material threading the
throat of the wormhole in dimensions), the material must still be
``exotic'', that is matter with a larger radial tension than total mass-energy
density multiplied by . Two specific solutions are applied to the general
cases and a partial stability analysis of a dimensional solution is
explored.Comment: 19 pgs. WATPHYS TH-93/0
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