Browsing by Author "Tereshchenko, Aleksandr"

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Automated classification of distributed graph problems
(2021-05-17) Tereshchenko, Aleksandr
Perustieteiden korkeakoulu | Master's thesis
The field of distributed computing and distributed algorithms is a well-established and quickly developing area of theoretical computer science. Similar to the study of traditional centralized algorithms, many researchers are particularly interested in understanding the complexity of distributed problems. In particular, over the last decade, the research community has had a series of breakthroughs in understanding the complexity landscape of locally checkable labeling problems (LCLs), which is one of the most significant and well-studied problem families in distributed computing. As more and more individual LCL problems have been understood, people started to investigate whether it was possible to automate the process. This led to a discovery of a whole range of so-called meta-algorithms. These are centralized algorithms that take a distributed LCL problem as their input and return information about its complexity as an output. Furthermore, many of the meta-algorithms turned out to be practical and were subsequently implemented as computer programs that can tell something useful about the complexities of LCL problems. The problem, however, is that these meta-algorithms are not currently used by the research community. This causes the scholars to solve the same problems that have been solved before. The reason for the failure to adopt the meta-algorithms is the fact that their implementations use different formalisms, which makes it inconvenient to use them in everyday work. The goal of the thesis is to resolve this problem and develop a solution that would unify the numerous meta-algorithms making it possible to benefit from them all while using only a single tool. In this work, I have developed a unified system that encapsulates most of the existing meta-algorithms, providing a unified interface to its users. I also implemented a Web interface to make the tool even more accessible for the community. Furthermore, I critically analyze the solution and propose ideas for its further improvement.
Brief Announcement: Temporal Locality in Online Algorithms
(2022-10-01) Pacut, Maciej; Parham, Mahmoud; Rybicki, Joel; Schmid, Stefan; Suomela, Jukka; Tereshchenko, Aleksandr
A4 Artikkeli konferenssijulkaisussa
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.
Locally checkable problems in rooted trees
(2023-09) Balliu, Alkida; Brandt, Sebastian; Chang, Yi Jun; Olivetti, Dennis; Studený, Jan; Suomela, Jukka; Tereshchenko, Aleksandr
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Consider any locally checkable labeling problem Π in rooted regular trees: there is a finite set of labels Σ , and for each label x∈ Σ we specify what are permitted label combinations of the children for an internal node of label x (the leaf nodes are unconstrained). This formalism is expressive enough to capture many classic problems studied in distributed computing, including vertex coloring, edge coloring, and maximal independent set. We show that the distributed computational complexity of any such problem Π falls in one of the following classes: it is O(1), Θ (log ∗n) , Θ (log n) , or nΘ (1) rounds in trees with n nodes (and all of these classes are nonempty). We show that the complexity of any given problem is the same in all four standard models of distributed graph algorithms: deterministic LOCAL, randomized LOCAL, deterministic CONGEST, and randomized CONGEST model. In particular, we show that randomness does not help in this setting, and the complexity class Θ (log log n) does not exist (while it does exist in the broader setting of general trees). We also show how to systematically determine the complexity class of any such problem Π , i.e., whether Π takes O(1), Θ (log ∗n) , Θ (log n) , or nΘ (1) rounds. While the algorithm may take exponential time in the size of the description of Π , it is nevertheless practical: we provide a freely available implementation of the classifier algorithm, and it is fast enough to classify many problems of interest.
Locally Checkable Problems in Rooted Trees
(2021-07-21) Balliu, Alkida; Brandt, Sebastian; Chang, Yi-Jun; Olivetti, Dennis; Studený, Jan; Suomela, Jukka; Tereshchenko, Aleksandr
A4 Artikkeli konferenssijulkaisussa
Consider any locally checkable labeling problem Π in rooted regular trees: there is a finite set of labels Σ, and for each label ∈ Σ we specify what are permitted label combinations of the children for an internal node of label (the leaf nodes are unconstrained). This formalism is expressive enough to capture many classic problems studied in distributed computing, including vertex coloring, edge coloring, and maximal independent set. We show that the distributed computational complexity of any such problem Π falls in one of the following classes: it is (1), Θ(log∗ ), Θ(log), or Θ(1) rounds in trees with nodes (and all of these classes are nonempty).We show that the complexity of any given problem is the same in all four standard models of distributed graph algorithms: deterministic LOCAL, randomized LOCAL, deterministic CONGEST, and randomized CONGEST model. In particular, we show that randomness does not help in this setting, and the complexity class Θ(log log) does not exist (while it does exist in the broader setting of general trees). We also show how to systematically determine the complexity class of any such problem Π, i.e., whether Π takes (1), Θ(log∗ ), Θ(log), or Θ(1) rounds. While the algorithm may take exponential time in the size of the description of Π, it is nevertheless practical: we provide a freely available implementation of the classifier algorithm, and it is fast enough to classify many problems of interest.