# 8 Search Results for "Sagunov, Danil"

Document
Track A: Algorithms, Complexity and Games
##### Approximating Long Cycle Above Dirac’s Guarantee

Authors: Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

##### Abstract
Parameterization above (or below) a guarantee is a successful concept in parameterized algorithms. The idea is that many computational problems admit "natural" guarantees bringing to algorithmic questions whether a better solution (above the guarantee) could be obtained efficiently. For example, for every boolean CNF formula on m clauses, there is an assignment that satisfies at least m/2 clauses. How difficult is it to decide whether there is an assignment satisfying more than m/2 + k clauses? Or, if an n-vertex graph has a perfect matching, then its vertex cover is at least n/2. Is there a vertex cover of size at least n/2 + k for some k ≥ 1 and how difficult is it to find such a vertex cover? The above guarantee paradigm has led to several exciting discoveries in the areas of parameterized algorithms and kernelization. We argue that this paradigm could bring forth fresh perspectives on well-studied problems in approximation algorithms. Our example is the longest cycle problem. One of the oldest results in extremal combinatorics is the celebrated Dirac’s theorem from 1952. Dirac’s theorem provides the following guarantee on the length of the longest cycle: for every 2-connected n-vertex graph G with minimum degree δ(G) ≤ n/2, the length of the longest cycle L is at least 2δ(G). Thus the "essential" part of finding the longest cycle is in approximating the "offset" k = L - 2δ(G). The main result of this paper is the above-guarantee approximation theorem for k. Informally, the theorem says that approximating the offset k is not harder than approximating the total length L of a cycle. In other words, for any (reasonably well-behaved) function f, a polynomial time algorithm constructing a cycle of length f(L) in an undirected graph with a cycle of length L, yields a polynomial time algorithm constructing a cycle of length 2δ(G)+Ω(f(k)).

##### Cite as

Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov. Approximating Long Cycle Above Dirac’s Guarantee. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 60:1-60:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

```@InProceedings{fomin_et_al:LIPIcs.ICALP.2023.60,
author =	{Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill},
title =	{{Approximating Long Cycle Above Dirac’s Guarantee}},
booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages =	{60:1--60:18},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-278-5},
ISSN =	{1868-8969},
year =	{2023},
volume =	{261},
editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.60},
URN =		{urn:nbn:de:0030-drops-181128},
doi =		{10.4230/LIPIcs.ICALP.2023.60},
annote =	{Keywords: Longest path, longest cycle, approximation algorithms, above guarantee parameterization, minimum degree, Dirac theorem}
}```
Document
##### Longest Cycle Above Erdős-Gallai Bound

Authors: Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

##### Abstract
In 1959, Erdős and Gallai proved that every graph G with average vertex degree ad(G) ≥ 2 contains a cycle of length at least ad(G). We provide an algorithm that for k ≥ 0 in time 2^𝒪(k)⋅n^𝒪(1) decides whether a 2-connected n-vertex graph G contains a cycle of length at least ad(G)+k. This resolves an open problem explicitly mentioned in several papers. The main ingredients of our algorithm are new graph-theoretical results interesting on their own.

##### Cite as

Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov. Longest Cycle Above Erdős-Gallai Bound. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 55:1-55:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

```@InProceedings{fomin_et_al:LIPIcs.ESA.2022.55,
author =	{Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill},
title =	{{Longest Cycle Above Erd\H{o}s-Gallai Bound}},
booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
pages =	{55:1--55:15},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-247-1},
ISSN =	{1868-8969},
year =	{2022},
volume =	{244},
editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.55},
URN =		{urn:nbn:de:0030-drops-169935},
doi =		{10.4230/LIPIcs.ESA.2022.55},
annote =	{Keywords: Longest path, longest cycle, fixed-parameter tractability, above guarantee parameterization, average degree, Erd\H{o}s and Gallai theorem}
}```
Document
Invited Talk
##### Long Cycles in Graphs: Extremal Combinatorics Meets Parameterized Algorithms (Invited Talk)

Authors: Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

##### Abstract
We discuss recent algorithmic extensions of two classic results of extremal combinatorics about long paths in graphs. First, the theorem of Dirac from 1952 asserts that a 2-connected graph G with the minimum vertex degree d > 1, is either Hamiltonian or contains a cycle of length at least 2d. Second, the theorem of Erdős-Gallai from 1959, states that a graph G with the average vertex degree D > 1, contains a cycle of length at least D. The proofs of these theorems are constructive, they provide polynomial-time algorithms constructing cycles of lengths 2d and D. We extend these algorithmic results by showing that each of the problems, to decide whether a 2-connected graph contains a cycle of length at least 2d+k or of a cycle of length at least D+k, is fixed-parameter tractable parameterized by k.

##### Cite as

Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov. Long Cycles in Graphs: Extremal Combinatorics Meets Parameterized Algorithms (Invited Talk). In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 1:1-1:4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

```@InProceedings{fomin_et_al:LIPIcs.MFCS.2022.1,
author =	{Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill},
title =	{{Long Cycles in Graphs: Extremal Combinatorics Meets Parameterized Algorithms}},
booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
pages =	{1:1--1:4},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-256-3},
ISSN =	{1868-8969},
year =	{2022},
volume =	{241},
editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.1},
URN =		{urn:nbn:de:0030-drops-167999},
doi =		{10.4230/LIPIcs.MFCS.2022.1},
annote =	{Keywords: Longest path, longest cycle, fixed-parameter tractability, above guarantee parameterization, average degree, dense graph, Dirac theorem, Erd\H{o}s-Gallai theorem}
}```
Document
##### Detours in Directed Graphs

Authors: Fedor V. Fomin, Petr A. Golovach, William Lochet, Danil Sagunov, Kirill Simonov, and Saket Saurabh

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

##### Abstract
We study two "above guarantee" versions of the classical Longest Path problem on undirected and directed graphs and obtain the following results. In the first variant of Longest Path that we study, called Longest Detour, the task is to decide whether a graph has an (s,t)-path of length at least dist_G(s,t)+k (where dist_G(s,t) denotes the length of a shortest path from s to t). Bezáková et al. [Ivona Bezáková et al., 2019] proved that on undirected graphs the problem is fixed-parameter tractable (FPT) by providing an algorithm of running time 2^{O(k)}⋅ n. Further, they left the parameterized complexity of the problem on directed graphs open. Our first main result establishes a connection between Longest Detour on directed graphs and 3-Disjoint Paths on directed graphs. Using these new insights, we design a 2^{O (k)}· n^{O(1)} time algorithm for the problem on directed planar graphs. Further, the new approach yields a significantly faster FPT algorithm on undirected graphs. In the second variant of Longest Path, namely Longest Path above Diameter, the task is to decide whether the graph has a path of length at least diam(G)+k(diam(G)denotes the length of a longest shortest path in a graph G). We obtain dichotomy results about Longest Path above Diameter on undirected and directed graphs. For (un)directed graphs, Longest Path above Diameter is NP-complete even for k=1. However, if the input undirected graph is 2-connected, then the problem is FPT. On the other hand, for 2-connected directed graphs, we show that Longest Path above Diameter is solvable in polynomial time for each k ∈ {1,..., 4} and is NP-complete for every k ≥ 5. The parameterized complexity of Longest Detour on general directed graphs remains an interesting open problem.

##### Cite as

Fedor V. Fomin, Petr A. Golovach, William Lochet, Danil Sagunov, Kirill Simonov, and Saket Saurabh. Detours in Directed Graphs. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 29:1-29:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

```@InProceedings{fomin_et_al:LIPIcs.STACS.2022.29,
author =	{Fomin, Fedor V. and Golovach, Petr A. and Lochet, William and Sagunov, Danil and Simonov, Kirill and Saurabh, Saket},
title =	{{Detours in Directed Graphs}},
booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
pages =	{29:1--29:16},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-222-8},
ISSN =	{1868-8969},
year =	{2022},
volume =	{219},
editor =	{Berenbrink, Petra and Monmege, Benjamin},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.29},
URN =		{urn:nbn:de:0030-drops-158390},
doi =		{10.4230/LIPIcs.STACS.2022.29},
annote =	{Keywords: longest path, longest detour, diameter, directed graphs, parameterized complexity}
}```
Document
##### Proof Complexity of Natural Formulas via Communication Arguments

Authors: Dmitry Itsykson and Artur Riazanov

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)

##### Abstract
A canonical communication problem Search(φ) is defined for every unsatisfiable CNF φ: an assignment to the variables of φ is partitioned among the communicating parties, they are to find a clause of φ falsified by this assignment. Lower bounds on the randomized k-party communication complexity of Search(φ) in the number-on-forehead (NOF) model imply tree-size lower bounds, rank lower bounds, and size-space tradeoffs for the formula φ in the semantic proof system T^{cc}(k,c) that operates with proof lines that can be computed by k-party randomized communication protocol using at most c bits of communication [Göös and Pitassi, 2014]. All known lower bounds on Search(φ) (e.g. [Beame et al., 2007; Göös and Pitassi, 2014; Russell Impagliazzo et al., 1994]) are realized on ad-hoc formulas φ (i.e. they were introduced specifically for these lower bounds). We introduce a new communication complexity approach that allows establishing proof complexity lower bounds for natural formulas. First, we demonstrate our approach for two-party communication and apply it to the proof system Res(⊕) that operates with disjunctions of linear equalities over 𝔽₂ [Dmitry Itsykson and Dmitry Sokolov, 2014]. Let a formula PM_G encode that a graph G has a perfect matching. If G has an odd number of vertices, then PM_G has a tree-like Res(⊕)-refutation of a polynomial-size [Dmitry Itsykson and Dmitry Sokolov, 2014]. It was unknown whether this is the case for graphs with an even number of vertices. Using our approach we resolve this question and show a lower bound 2^{Ω(n)} on size of tree-like Res(⊕)-refutations of PM_{K_{n+2,n}}. Then we apply our approach for k-party communication complexity in the NOF model and obtain a Ω(1/k 2^{n/2k - 3k/2}) lower bound on the randomized k-party communication complexity of Search(BPHP^{M}_{2ⁿ}) w.r.t. to some natural partition of the variables, where BPHP^{M}_{2ⁿ} is the bit pigeonhole principle and M = 2ⁿ+2^{n(1-1/k)}. In particular, our result implies that the bit pigeonhole requires exponential tree-like Th(k) proofs, where Th(k) is the semantic proof system operating with polynomial inequalities of degree at most k and k = 𝒪(log^{1-ε} n) for some ε > 0. We also show that BPHP^{2ⁿ+1}_{2ⁿ} superpolynomially separates tree-like Th(log^{1-ε} m) from tree-like Th(log m), where m is the number of variables in the refuted formula.

##### Cite as

Dmitry Itsykson and Artur Riazanov. Proof Complexity of Natural Formulas via Communication Arguments. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 3:1-3:34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

```@InProceedings{itsykson_et_al:LIPIcs.CCC.2021.3,
author =	{Itsykson, Dmitry and Riazanov, Artur},
title =	{{Proof Complexity of Natural Formulas via Communication Arguments}},
booktitle =	{36th Computational Complexity Conference (CCC 2021)},
pages =	{3:1--3:34},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-193-1},
ISSN =	{1868-8969},
year =	{2021},
volume =	{200},
editor =	{Kabanets, Valentine},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.3},
URN =		{urn:nbn:de:0030-drops-142773},
doi =		{10.4230/LIPIcs.CCC.2021.3},
annote =	{Keywords: bit pigeonhole principle, disjointness, multiparty communication complexity, perfect matching, proof complexity, randomized communication complexity, Resolution over linear equations, tree-like proofs}
}```
Document
##### Diverse Pairs of Matchings

Authors: Fedor V. Fomin, Petr A. Golovach, Lars Jaffke, Geevarghese Philip, and Danil Sagunov

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

##### Abstract
We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph G and an integer k, ask whether G has two (maximum/perfect) matchings whose symmetric difference is at least k. Diverse Pair of Matchings (asking for two not necessarily maximum or perfect matchings) is NP-complete on general graphs if k is part of the input, and we consider two restricted variants. First, we show that on bipartite graphs, the problem is polynomial-time solvable, and second we show that Diverse Pair of Maximum Matchings is FPT parameterized by k. We round off the work by showing that Diverse Pair of Matchings has a kernel on 𝒪(k²) vertices.

##### Cite as

Fedor V. Fomin, Petr A. Golovach, Lars Jaffke, Geevarghese Philip, and Danil Sagunov. Diverse Pairs of Matchings. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 26:1-26:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

```@InProceedings{fomin_et_al:LIPIcs.ISAAC.2020.26,
author =	{Fomin, Fedor V. and Golovach, Petr A. and Jaffke, Lars and Philip, Geevarghese and Sagunov, Danil},
title =	{{Diverse Pairs of Matchings}},
booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
pages =	{26:1--26:12},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-173-3},
ISSN =	{1868-8969},
year =	{2020},
volume =	{181},
editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.26},
URN =		{urn:nbn:de:0030-drops-133706},
doi =		{10.4230/LIPIcs.ISAAC.2020.26},
annote =	{Keywords: Matching, Solution Diversity, Fixed-Parameter Tractability}
}```
Document
##### Building Large k-Cores from Sparse Graphs

Authors: Fedor V. Fomin, Danil Sagunov, and Kirill Simonov

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

##### Abstract
A popular model to measure network stability is the k-core, that is the maximal induced subgraph in which every vertex has degree at least k. For example, k-cores are commonly used to model the unraveling phenomena in social networks. In this model, users having less than k connections within the network leave it, so the remaining users form exactly the k-core. In this paper we study the question of whether it is possible to make the network more robust by spending only a limited amount of resources on new connections. A mathematical model for the k-core construction problem is the following Edge k-Core optimization problem. We are given a graph G and integers k, b and p. The task is to ensure that the k-core of G has at least p vertices by adding at most b edges. The previous studies on Edge k-Core demonstrate that the problem is computationally challenging. In particular, it is NP-hard when k = 3, W-hard when parameterized by k+b+p (Chitnis and Talmon, 2018), and APX-hard (Zhou et al, 2019). Nevertheless, we show that there are efficient algorithms with provable guarantee when the k-core has to be constructed from a sparse graph with some additional structural properties. Our results are - When the input graph is a forest, Edge k-Core is solvable in polynomial time; - Edge k-Core is fixed-parameter tractable (FPT) when parameterized by the minimum size of a vertex cover in the input graph. On the other hand, with such parameterization, the problem does not admit a polynomial kernel subject to a widely-believed assumption from complexity theory; - Edge k-Core is FPT parameterized by the treewidth of the graph plus k. This improves upon a result of Chitnis and Talmon by not requiring b to be small. Each of our algorithms is built upon a new graph-theoretical result interesting in its own.

##### Cite as

Fedor V. Fomin, Danil Sagunov, and Kirill Simonov. Building Large k-Cores from Sparse Graphs. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 35:1-35:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

```@InProceedings{fomin_et_al:LIPIcs.MFCS.2020.35,
author =	{Fomin, Fedor V. and Sagunov, Danil and Simonov, Kirill},
title =	{{Building Large k-Cores from Sparse Graphs}},
booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
pages =	{35:1--35:14},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-159-7},
ISSN =	{1868-8969},
year =	{2020},
volume =	{170},
editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.35},
URN =		{urn:nbn:de:0030-drops-127026},
doi =		{10.4230/LIPIcs.MFCS.2020.35},
annote =	{Keywords: parameterized complexity, k-core, vertex cover, treewidth}
}```
Document
##### Solving Target Set Selection with Bounded Thresholds Faster than 2^n

Authors: Ivan Bliznets and Danil Sagunov

Published in: LIPIcs, Volume 115, 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)

##### Abstract
In this paper we consider the Target Set Selection problem. The problem naturally arises in many fields like economy, sociology, medicine. In the Target Set Selection problem one is given a graph G with a function thr: V(G) -> N cup {0} and integers k, l. The goal of the problem is to activate at most k vertices initially so that at the end of the activation process there is at least l activated vertices. The activation process occurs in the following way: (i) once activated, a vertex stays activated forever; (ii) vertex v becomes activated if at least thr(v) of its neighbours are activated. The problem and its different special cases were extensively studied from approximation and parameterized points of view. For example, parameterizations by the following parameters were studied: treewidth, feedback vertex set, diameter, size of target set, vertex cover, cluster editing number and others. Despite the extensive study of the problem it is still unknown whether the problem can be solved in O^*((2-epsilon)^n) time for some epsilon >0. We partially answer this question by presenting several faster-than-trivial algorithms that work in cases of constant thresholds, constant dual thresholds or when the threshold value of each vertex is bounded by one-third of its degree. Also, we show that the problem parameterized by l is W-hard even when all thresholds are constant.

##### Cite as

Ivan Bliznets and Danil Sagunov. Solving Target Set Selection with Bounded Thresholds Faster than 2^n. In 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 115, pp. 22:1-22:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

```@InProceedings{bliznets_et_al:LIPIcs.IPEC.2018.22,
author =	{Bliznets, Ivan and Sagunov, Danil},
title =	{{Solving Target Set Selection with Bounded Thresholds Faster than 2^n}},
booktitle =	{13th International Symposium on Parameterized and Exact Computation (IPEC 2018)},
pages =	{22:1--22:14},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-084-2},
ISSN =	{1868-8969},
year =	{2019},
volume =	{115},
editor =	{Paul, Christophe and Pilipczuk, Michal},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2018.22},
URN =		{urn:nbn:de:0030-drops-102235},
doi =		{10.4230/LIPIcs.IPEC.2018.22},
annote =	{Keywords: exact exponential algorithms, target set, vertex thresholds, social influence, irreversible conversions of graphs, bootstrap percolation}
}```
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