Academic Journal
The Message Complexity of Distributed Graph Optimization
| Τίτλος: | The Message Complexity of Distributed Graph Optimization |
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| Συγγραφείς: | Dufoulon, Fabien, Pai, Shreyas, Pandurangan, Gopal, Pemmaraju, Sriram V., Robinson, Peter |
| Συνεισφορές: | Fabien Dufoulon and Shreyas Pai and Gopal Pandurangan and Sriram V. Pemmaraju and Peter Robinson |
| Στοιχεία εκδότη: | Schloss Dagstuhl – Leibniz-Zentrum für Informatik |
| Έτος έκδοσης: | 2024 |
| Συλλογή: | DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics ) |
| Θεματικοί όροι: | Distributed graph algorithm, message complexity, distributed approximation |
| Περιγραφή: | The message complexity of a distributed algorithm is the total number of messages sent by all nodes over the course of the algorithm. This paper studies the message complexity of distributed algorithms for fundamental graph optimization problems. We focus on four classical graph optimization problems: Maximum Matching (MaxM), Minimum Vertex Cover (MVC), Minimum Dominating Set (MDS), and Maximum Independent Set (MaxIS). In the sequential setting, these problems are representative of a wide spectrum of hardness of approximation. While there has been some progress in understanding the round complexity of distributed algorithms (for both exact and approximate versions) for these problems, much less is known about their message complexity and its relation with the quality of approximation. We almost fully quantify the message complexity of distributed graph optimization by showing the following results: 1) Cubic regime: Our first main contribution is showing essentially cubic, i.e., Ω̃(n³) lower bounds (where n is the number of nodes in the graph) on the message complexity of distributed exact computation of Minimum Vertex Cover (MVC), Minimum Dominating Set (MDS), and Maximum Independent Set (MaxIS). Our lower bounds apply to any distributed algorithm that runs in polynomial number of rounds (a mild and necessary restriction). Our result is significant since, to the best of our knowledge, this are the first ω(m) (where m is the number of edges in the graph) message lower bound known for distributed computation of such classical graph optimization problems. Our bounds are essentially tight, as all these problems can be solved trivially using O(n³) messages in polynomial rounds. All these bounds hold in the standard CONGEST model of distributed computation in which messages are of O(log n) size. 2) Quadratic regime: In contrast, we show that if we allow approximate computation then Θ̃(n²) messages are both necessary and sufficient. Specifically, we show that Ω̃(n²) messages are required for constant-factor ... |
| Τύπος εγγράφου: | article in journal/newspaper conference object |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| Relation: | Is Part Of LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.41 |
| DOI: | 10.4230/LIPIcs.ITCS.2024.41 |
| Διαθεσιμότητα: | https://doi.org/10.4230/LIPIcs.ITCS.2024.41 https://nbn-resolving.org/urn:nbn:de:0030-drops-195690 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.41 |
| Rights: | https://creativecommons.org/licenses/by/4.0/legalcode |
| Αριθμός Καταχώρησης: | edsbas.A475EEF |
| Βάση Δεδομένων: | BASE |
| DOI: | 10.4230/LIPIcs.ITCS.2024.41 |
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