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Documents authored by Pupyrev, Sergey


Document
The Price of Upwardness

Authors: Patrizio Angelini, Therese Biedl, Markus Chimani, Sabine Cornelsen, Giordano Da Lozzo, Seok-Hee Hong, Giuseppe Liotta, Maurizio Patrignani, Sergey Pupyrev, Ignaz Rutter, and Alexander Wolff

Published in: LIPIcs, Volume 320, 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)


Abstract
Not every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward k-planar drawings of DAGs in which the edges are monotonically increasing in a common direction and every edge is crossed at most k times for some integer k ≥ 1. We show that the number of crossings per edge in a monotone drawing is in general unbounded for the class of bipartite outerplanar, cubic, or bounded pathwidth DAGs. However, it is at most two for outerpaths and it is at most quadratic in the bandwidth in general. From the computational point of view, we prove that upward-k-planarity testing is NP-complete already for k = 1 and even for restricted instances for which upward planarity testing is polynomial. On the positive side, we can decide in linear time whether a single-source DAG admits an upward 1-planar drawing in which all vertices are incident to the outer face.

Cite as

Patrizio Angelini, Therese Biedl, Markus Chimani, Sabine Cornelsen, Giordano Da Lozzo, Seok-Hee Hong, Giuseppe Liotta, Maurizio Patrignani, Sergey Pupyrev, Ignaz Rutter, and Alexander Wolff. The Price of Upwardness. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{angelini_et_al:LIPIcs.GD.2024.13,
  author =	{Angelini, Patrizio and Biedl, Therese and Chimani, Markus and Cornelsen, Sabine and Da Lozzo, Giordano and Hong, Seok-Hee and Liotta, Giuseppe and Patrignani, Maurizio and Pupyrev, Sergey and Rutter, Ignaz and Wolff, Alexander},
  title =	{{The Price of Upwardness}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.13},
  URN =		{urn:nbn:de:0030-drops-212977},
  doi =		{10.4230/LIPIcs.GD.2024.13},
  annote =	{Keywords: upward drawings, beyond planarity, upward k-planarity, upward outer-1-planarity}
}
Document
Approximating the Minimum Logarithmic Arrangement Problem

Authors: Julián Mestre and Sergey Pupyrev

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)


Abstract
We study a graph reordering problem motivated by compressing massive graphs such as social networks and inverted indexes. Given a graph, G = (V, E), the Minimum Logarithmic Arrangement problem is to find a permutation, π, of the vertices that minimizes ∑_{(u, v) ∈ E} (1 + ⌊ lg |π(u) - π(v)| ⌋). This objective has been shown to be a good measure of how many bits are needed to encode the graph if the adjacency list of each vertex is encoded using relative positions of two consecutive neighbors under the π order in the list rather than using absolute indices or node identifiers, which requires at least lg n bits per edge. We show the first non-trivial approximation factor for this problem by giving a polynomial time 𝒪(log k)-approximation algorithm for graphs with treewidth k.

Cite as

Julián Mestre and Sergey Pupyrev. Approximating the Minimum Logarithmic Arrangement Problem. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{mestre_et_al:LIPIcs.ISAAC.2022.7,
  author =	{Mestre, Juli\'{a}n and Pupyrev, Sergey},
  title =	{{Approximating the Minimum Logarithmic Arrangement Problem}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.7},
  URN =		{urn:nbn:de:0030-drops-172924},
  doi =		{10.4230/LIPIcs.ISAAC.2022.7},
  annote =	{Keywords: approximation algorithms, graph compression}
}
Document
On the Extended TSP Problem

Authors: Julián Mestre, Sergey Pupyrev, and Seeun William Umboh

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)


Abstract
We initiate the theoretical study of Ext-TSP, a problem that originates in the area of profile-guided binary optimization. Given a graph G = (V, E) with positive edge weights w: E → R^+, and a non-increasing discount function f(⋅) such that f(1) = 1 and f(i) = 0 for i > k, for some parameter k that is part of the problem definition. The problem is to sequence the vertices V so as to maximize ∑_{(u, v) ∈ E} f(|d_u - d_v|)⋅ w(u,v), where d_v ∈ {1, …, |V|} is the position of vertex v in the sequence. We show that Ext-TSP is APX-hard to approximate in general and we give a (k+1)-approximation algorithm for general graphs and a PTAS for some sparse graph classes such as planar or treewidth-bounded graphs. Interestingly, the problem remains challenging even on very simple graph classes; indeed, there is no exact n^o(k) time algorithm for trees unless the ETH fails. We complement this negative result with an exact n^O(k) time algorithm for trees.

Cite as

Julián Mestre, Sergey Pupyrev, and Seeun William Umboh. On the Extended TSP Problem. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 42:1-42:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{mestre_et_al:LIPIcs.ISAAC.2021.42,
  author =	{Mestre, Juli\'{a}n and Pupyrev, Sergey and Umboh, Seeun William},
  title =	{{On the Extended TSP Problem}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{42:1--42:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.42},
  URN =		{urn:nbn:de:0030-drops-154751},
  doi =		{10.4230/LIPIcs.ISAAC.2021.42},
  annote =	{Keywords: profile-guided optimization, approximation algorithms, bandwidth, TSP}
}
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