@article{12566, abstract = {Approximate agreement is one of the few variants of consensus that can be solved in a wait-free manner in asynchronous systems where processes communicate by reading and writing to shared memory. In this work, we consider a natural generalisation of approximate agreement on arbitrary undirected connected graphs. Each process is given a node of the graph as input and, if non-faulty, must output a node such that – all the outputs are within distance 1 of one another, and – each output value lies on a shortest path between two input values. From prior work, it is known that there is no wait-free algorithm among processes for this problem on any cycle of length , by reduction from 2-set agreement (Castañeda et al., 2018). In this work, we investigate the solvability of this task on general graphs. We give a new, direct proof of the impossibility of approximate agreement on cycles of length , via a generalisation of Sperner's Lemma to convex polygons. We also extend the reduction from 2-set agreement to a larger class of graphs, showing that approximate agreement on these graphs is unsolvable. On the positive side, we present a wait-free algorithm for a different class of graphs, which properly contains the class of chordal graphs.}, author = {Alistarh, Dan-Adrian and Ellen, Faith and Rybicki, Joel}, issn = {0304-3975}, journal = {Theoretical Computer Science}, number = {2}, publisher = {Elsevier}, title = {{Wait-free approximate agreement on graphs}}, doi = {10.1016/j.tcs.2023.113733}, volume = {948}, year = {2023}, } @inproceedings{11184, abstract = {Let G be a graph on n nodes. In the stochastic population protocol model, a collection of n indistinguishable, resource-limited nodes collectively solve tasks via pairwise interactions. In each interaction, two randomly chosen neighbors first read each other’s states, and then update their local states. A rich line of research has established tight upper and lower bounds on the complexity of fundamental tasks, such as majority and leader election, in this model, when G is a clique. Specifically, in the clique, these tasks can be solved fast, i.e., in n polylog n pairwise interactions, with high probability, using at most polylog n states per node. In this work, we consider the more general setting where G is an arbitrary regular graph, and present a technique for simulating protocols designed for fully-connected networks in any connected regular graph. Our main result is a simulation that is efficient on many interesting graph families: roughly, the simulation overhead is polylogarithmic in the number of nodes, and quadratic in the conductance of the graph. As a sample application, we show that, in any regular graph with conductance φ, both leader election and exact majority can be solved in φ^{-2} ⋅ n polylog n pairwise interactions, with high probability, using at most φ^{-2} ⋅ polylog n states per node. This shows that there are fast and space-efficient population protocols for leader election and exact majority on graphs with good expansion properties. We believe our results will prove generally useful, as they allow efficient technology transfer between the well-mixed (clique) case, and the under-explored spatial setting.}, author = {Alistarh, Dan-Adrian and Gelashvili, Rati and Rybicki, Joel}, booktitle = {25th International Conference on Principles of Distributed Systems}, editor = {Bramas, Quentin and Gramoli, Vincent and Milani, Alessia}, isbn = {9783959772198}, issn = {1868-8969}, location = {Strasbourg, France}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Fast graphical population protocols}}, doi = {10.4230/LIPIcs.OPODIS.2021.14}, volume = {217}, year = {2022}, } @inproceedings{11707, abstract = {In this work we introduce the graph-theoretic notion of mendability: for each locally checkable graph problem we can define its mending radius, which captures the idea of how far one needs to modify a partial solution in order to “patch a hole.” We explore how mendability is connected to the existence of efficient algorithms, especially in distributed, parallel, and fault-tolerant settings. It is easy to see that O(1)-mendable problems are also solvable in O(log∗n) rounds in the LOCAL model of distributed computing. One of the surprises is that in paths and cycles, a converse also holds in the following sense: if a problem Π can be solved in O(log∗n), there is always a restriction Π′⊆Π that is still efficiently solvable but that is also O(1)-mendable. We also explore the structure of the landscape of mendability. For example, we show that in trees, the mending radius of any locally checkable problem is O(1), Θ(logn), or Θ(n), while in general graphs the structure is much more diverse.}, author = {Balliu, Alkida and Hirvonen, Juho and Melnyk, Darya and Olivetti, Dennis and Rybicki, Joel and Suomela, Jukka}, booktitle = {International Colloquium on Structural Information and Communication Complexity}, editor = {Parter, Merav}, isbn = {9783031099922}, issn = {1611-3349}, location = {Paderborn, Germany}, pages = {1--20}, publisher = {Springer Nature}, title = {{Local mending}}, doi = {10.1007/978-3-031-09993-9_1}, volume = {13298}, year = {2022}, } @inproceedings{12182, abstract = {Online algorithms make decisions based on past inputs, with the goal of being competitive against an algorithm that sees also future inputs. In this work, we introduce time-local online algorithms; these are online algorithms in which the output at any given time is a function of only T latest inputs. Our main observation is that time-local online algorithms are closely connected to local distributed graph algorithms: distributed algorithms make decisions based on the local information in the spatial dimension, while time-local online algorithms make decisions based on the local information in the temporal dimension. We formalize this connection, and show how we can directly use the tools developed to study distributed approximability of graph optimization problems to prove upper and lower bounds on the competitive ratio achieved with time-local online algorithms. Moreover, we show how to use computational techniques to synthesize optimal time-local algorithms.}, author = {Pacut, Maciej and Parham, Mahmoud and Rybicki, Joel and Schmid, Stefan and Suomela, Jukka and Tereshchenko, Aleksandr}, booktitle = {36th International Symposium on Distributed Computing}, issn = {1868-8969}, location = {Augusta, GA, United States}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Brief announcement: Temporal locality in online algorithms}}, doi = {10.4230/LIPIcs.DISC.2022.52}, volume = {246}, year = {2022}, } @inproceedings{10854, abstract = {Consider a distributed task where the communication network is fixed but the local inputs given to the nodes of the distributed system may change over time. In this work, we explore the following question: if some of the local inputs change, can an existing solution be updated efficiently, in a dynamic and distributed manner? To address this question, we define the batch dynamic CONGEST model in which we are given a bandwidth-limited communication network and a dynamic edge labelling defines the problem input. The task is to maintain a solution to a graph problem on the labelled graph under batch changes. We investigate, when a batch of alpha edge label changes arrive, - how much time as a function of alpha we need to update an existing solution, and - how much information the nodes have to keep in local memory between batches in order to update the solution quickly. Our work lays the foundations for the theory of input-dynamic distributed network algorithms. We give a general picture of the complexity landscape in this model, design both universal algorithms and algorithms for concrete problems, and present a general framework for lower bounds. The diverse time complexity of our model spans from constant time, through time polynomial in alpha, and to alpha time, which we show to be enough for any task.}, author = {Foerster, Klaus-Tycho and Korhonen, Janne and Paz, Ami and Rybicki, Joel and Schmid, Stefan}, booktitle = {Abstract Proceedings of the 2021 ACM SIGMETRICS / International Conference on Measurement and Modeling of Computer Systems}, isbn = {9781450380720}, location = {Virtual, Online}, pages = {71--72}, publisher = {Association for Computing Machinery}, title = {{Input-dynamic distributed algorithms for communication networks}}, doi = {10.1145/3410220.3453923}, year = {2021}, } @article{10855, abstract = {Consider a distributed task where the communication network is fixed but the local inputs given to the nodes of the distributed system may change over time. In this work, we explore the following question: if some of the local inputs change, can an existing solution be updated efficiently, in a dynamic and distributed manner? To address this question, we define the batch dynamic \congest model in which we are given a bandwidth-limited communication network and a dynamic edge labelling defines the problem input. The task is to maintain a solution to a graph problem on the labeled graph under batch changes. We investigate, when a batch of α edge label changes arrive, \beginitemize \item how much time as a function of α we need to update an existing solution, and \item how much information the nodes have to keep in local memory between batches in order to update the solution quickly. \enditemize Our work lays the foundations for the theory of input-dynamic distributed network algorithms. We give a general picture of the complexity landscape in this model, design both universal algorithms and algorithms for concrete problems, and present a general framework for lower bounds. In particular, we derive non-trivial upper bounds for two selected, contrasting problems: maintaining a minimum spanning tree and detecting cliques.}, author = {Foerster, Klaus-Tycho and Korhonen, Janne and Paz, Ami and Rybicki, Joel and Schmid, Stefan}, issn = {2476-1249}, journal = {Proceedings of the ACM on Measurement and Analysis of Computing Systems}, keywords = {Computer Networks and Communications, Hardware and Architecture, Safety, Risk, Reliability and Quality, Computer Science (miscellaneous)}, number = {1}, pages = {1--33}, publisher = {Association for Computing Machinery}, title = {{Input-dynamic distributed algorithms for communication networks}}, doi = {10.1145/3447384}, volume = {5}, year = {2021}, } @inproceedings{9678, abstract = {We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for stable orientations and more generally for locally optimal semi-matchings. The prior work by Czygrinow et al. (DISC 2012) finds a stable orientation in O(Δ^5) rounds in graphs of maximum degree Δ, while we improve it to O(Δ^4) and also prove a lower bound of Ω(Δ). For the more general problem of locally optimal semi-matchings, the prior upper bound is O(S^5) and our new algorithm runs in O(C · S^4) rounds, which is an improvement for C = o(S); here C and S are the maximum degrees of customers and servers, respectively.}, author = {Brandt, Sebastian and Keller, Barbara and Rybicki, Joel and Suomela, Jukka and Uitto, Jara}, booktitle = {Annual ACM Symposium on Parallelism in Algorithms and Architectures}, isbn = {9781450380706}, location = { Virtual Event, United States}, pages = {129--139}, title = {{Efficient load-balancing through distributed token dropping}}, doi = {10.1145/3409964.3461785}, year = {2021}, } @inproceedings{10218, abstract = {Let G be a graph on n nodes. In the stochastic population protocol model, a collection of n indistinguishable, resource-limited nodes collectively solve tasks via pairwise interactions. In each interaction, two randomly chosen neighbors first read each other’s states, and then update their local states. A rich line of research has established tight upper and lower bounds on the complexity of fundamental tasks, such as majority and leader election, in this model, when G is a clique. Specifically, in the clique, these tasks can be solved fast, i.e., in n polylog n pairwise interactions, with high probability, using at most polylog n states per node. In this work, we consider the more general setting where G is an arbitrary graph, and present a technique for simulating protocols designed for fully-connected networks in any connected regular graph. Our main result is a simulation that is efficient on many interesting graph families: roughly, the simulation overhead is polylogarithmic in the number of nodes, and quadratic in the conductance of the graph. As an example, this implies that, in any regular graph with conductance φ, both leader election and exact majority can be solved in φ^{-2} ⋅ n polylog n pairwise interactions, with high probability, using at most φ^{-2} ⋅ polylog n states per node. This shows that there are fast and space-efficient population protocols for leader election and exact majority on graphs with good expansion properties.}, author = {Alistarh, Dan-Adrian and Gelashvili, Rati and Rybicki, Joel}, booktitle = {35th International Symposium on Distributed Computing}, isbn = {9-783-9597-7210-5}, issn = {1868-8969}, location = {Freiburg, Germany}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Brief announcement: Fast graphical population protocols}}, doi = {10.4230/LIPIcs.DISC.2021.43}, volume = {209}, year = {2021}, } @article{7224, abstract = {Habitat loss is one of the key drivers of the ongoing decline of biodiversity. However, ecologists still argue about how fragmentation of habitat (independent of habitat loss) affects species richness. The recently proposed habitat amount hypothesis posits that species richness only depends on the total amount of habitat in a local landscape. In contrast, empirical studies report contrasting patterns: some find positive and others negative effects of fragmentation per se on species richness. To explain this apparent disparity, we devise a stochastic, spatially explicit model of competitive species communities in heterogeneous habitats. The model shows that habitat loss and fragmentation have complex effects on species diversity in competitive communities. When the total amount of habitat is large, fragmentation per se tends to increase species diversity, but if the total amount of habitat is small, the situation is reversed: fragmentation per se decreases species diversity.}, author = {Rybicki, Joel and Abrego, Nerea and Ovaskainen, Otso}, issn = {1461-0248}, journal = {Ecology Letters}, number = {3}, pages = {506--517}, publisher = {Wiley}, title = {{Habitat fragmentation and species diversity in competitive communities}}, doi = {10.1111/ele.13450}, volume = {23}, year = {2020}, }