• Corpus ID: 246680005

Shortest Paths without a Map, but with an Entropic Regularizer

@article{Bubeck2022ShortestPW,
  title={Shortest Paths without a Map, but with an Entropic Regularizer},
  author={S{\'e}bastien Bubeck and Christian Coester and Yuval Rabani},
  journal={ArXiv},
  year={2022},
  volume={abs/2202.04551}
}
In a 1989 paper titled “shortest paths without a map”, Papadimitriou and Yannakakis introduced an online model of searching in a weighted layered graph for a target node, while attempting to minimize the total length of the path traversed by the searcher. This problem, later called layered graph traversal, is parametrized by the maximum cardinality : of a layer of the input graph. It is an online setting for dynamic programming, and it is known to be a rather general and fundamental model of… 

References

SHOWING 1-10 OF 30 REFERENCES
On traversing layered graphs on-line
The following bounds on the competitive ratios of deterministic and randomized on-line algorithms for traversing width-w layered graphs are obtained. ?A deterministic algorithm with a competitive
On the History of the Shortest Path Problem
TLDR
Compared with other combinatorial optimization problems, like shortest spanning tree, assignment and transportation, the mathematical research in the shortest path problem started relatively late, which might be due to the fact that the problem is elementary and relatively easy.
Shortest Paths Without a Map
Competitive algorithms for layered graph traversal
TLDR
For traversing layered graphs consisting of w disjoint paths tied together at a common source, the authors give a randomized online algorithm with a competitive ratio of O(log w) and prove that this is optimal up to a constant factor.
Fusible HSTs and the Randomized k-Server Conjecture
  • James R. Lee
  • Computer Science, Mathematics
    2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2018
TLDR
A poly(log k)-competitive randomized algorithm for the k-server problem on any metric space that maintains an approximation of the underlying metric space by a distribution over HSTs and adjusts the granularity and accuracy according to the aggregate behavior of the HST algorithms.
Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem
Searching for a goal is a central and extensively studied problem in computer science. In classical searching problems, the cost of a search function is simply the number of queries made to an oracle
Learning-Augmented Weighted Paging
We consider a natural semi-online model for weighted paging, where at any time the algorithm is given predictions, possibly with errors, about the next arrival of each page. The model is inspired by
Pure entropic regularization for metrical task systems
TLDR
This work shows that on every HST metric, there is a randomized online algorithm for metrical task systems (MTS) that is 1-competitive for service costs and O(\log n)- competitive for movement costs and satisfies a set of refined guarantees.
Traversing Layered Graphs Using the Work Function Algorithm
The work function algorithm (WFA) is an on-line algorithm that has been studied mostly in connection with thek-server problem, but can actually be used on a wide variety of on-line problems. Despite
Online metric allocation
TLDR
A key idea of this algorithm is to decouple the rate at which a variable is updated from its value, resulting in interesting new dynamics, which can be viewed as running mirror descent with a time-varying regularizer, and used to further refine the guarantees of the algorithm.
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