Local Distributed Rounding: Generalized to MIS, Matching, Set Cover, and Beyond
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10515280" target="_blank" >RIV/00216208:11320/25:10515280 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=n~_8kV90Oh" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=n~_8kV90Oh</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/3742476" target="_blank" >10.1145/3742476</a>
Alternative languages
Result language
angličtina
Original language name
Local Distributed Rounding: Generalized to MIS, Matching, Set Cover, and Beyond
Original language description
We develop a general deterministic distributed method for locally rounding fractional solutions of graph problems for which the analysis can be broken down into analyzing pairs of vertices. Roughly speaking, the method can transform fractional/probabilistic label assignments of the vertices into integral/deterministic label assignments for the vertices, while approximately preserving a potential function that is a linear combination of functions, each of which depends on at most two vertices (subject to some conditions usually satisfied in pairwise analyses). The method unifies and significantly generalizes prior work on deterministic local rounding obtain polylogarithmic-time deterministic distributed solutions for combinatorial graph problems. Our general rounding result enables us to locally and efficiently derandomize a range of distributed algorithms for local and minimum-cost set cover approximation. As highlights, we, in particular, obtain the following results. -We obtain a deterministic O (log(2) Delta <middle dot> log n)-round algorithm for computing an MIS in the LOCAL model and an almost as efficient O (log(2) Delta <middle dot> log log Delta <middle dot> log n)-round deterministic MIS algorithm in the CONGEST model. As a result, the best known deterministic distributed time complexity of the four most widely studied distributed symmetry breaking problems (MIS, maximal matching, (Delta + 1)-vertex coloring, and (2 Delta - 1)-edge coloring) is now O (log(2) Delta <middle dot> log n). Our new MIS algorithm is also the first direct polylogarithmic-time deterministic distributed MIS algorithm, which is not based on network decomposition. -We obtain efficient deterministic distributed algorithms for rounding fractional solutions for maximum (weighted) independent set and minimum (weighted) set cover. In particular, for any constant epsilon > 0, we give a deterministic O (log(2) A + log* n)-round algorithm for computing an independent set of size (1/2 -epsilon) <middle dot> n/deg(avg), and we give deterministic O(log(2)(Delta W) + log* n)-round algorithms for computing a (1 - epsilon)/Delta-approximation of maximum weight independent set, and for computing a (1 - epsilon)/r-approximation of maximum weight matching in hypergraphs of rank r. For minimum set cover instances with sets of size at most sand where each element is contained in at most t sets, we show that an O (log s)-approximation can be computed in time O (log s <middle dot> log(2) t + log(& lowast; )n).
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ACM Transactions on Algorithms
ISSN
1549-6325
e-ISSN
1549-6333
Volume of the periodical
21
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
48
Pages from-to
42
UT code for WoS article
001576309200012
EID of the result in the Scopus database
2-s2.0-105018673577