Merino, Arturo I. ;
Soto, José A.
The Minimum Cost Query Problem on Matroids with Uncertainty Areas
Abstract
We study the minimum weight basis problem on matroid when elements' weights are uncertain. For each element we only know a set of possible values (an uncertainty area) that contains its real weight. In some cases there exist bases that are uniformly optimal, that is, they are minimum weight bases for every possible weight function obeying the uncertainty areas. In other cases, computing such a basis is not possible unless we perform some queries for the exact value of some elements.
Our main result is a polynomial time algorithm for the following problem. Given a matroid with uncertainty areas and a query cost function on its elements, find the set of elements of minimum total cost that we need to simultaneously query such that, no matter their revelation, the resulting instance admits a uniformly optimal base. We also provide combinatorial characterizations of all uniformly optimal bases, when one exists; and of all sets of queries that can be performed so that after revealing the corresponding weights the resulting instance admits a uniformly optimal base.
BibTeX  Entry
@InProceedings{merino_et_al:LIPIcs:2019:10659,
author = {Arturo I. Merino and Jos{\'e} A. Soto},
title = {{The Minimum Cost Query Problem on Matroids with Uncertainty Areas}},
booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
pages = {83:183:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771092},
ISSN = {18688969},
year = {2019},
volume = {132},
editor = {Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10659},
URN = {urn:nbn:de:0030drops106592},
doi = {10.4230/LIPIcs.ICALP.2019.83},
annote = {Keywords: Minimum spanning tree, matroids, uncertainty, queries}
}
2019
Keywords: 

Minimum spanning tree, matroids, uncertainty, queries 
Seminar: 

46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Issue date: 

2019 
Date of publication: 

2019 