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Documents authored by Husić, Edin

Document
DOI: 10.4230/LIPIcs.SoCG.2024.61
Approximating the Maximum Independent Set of Convex Polygons with a Bounded Number of Directions

Authors: Fabrizio Grandoni, Edin Husić, Mathieu Mari, and Antoine Tinguely

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract
In the maximum independent set of convex polygons problem, we are given a set of n convex polygons in the plane with the objective of selecting a maximum cardinality subset of non-overlapping polygons. Here we study a special case of the problem where the edges of the polygons can take at most d fixed directions. We present an 8d/3-approximation algorithm for this problem running in time O((nd)^O(d4^d)). The previous-best polynomial-time approximation (for constant d) was a classical n^ε approximation by Fox and Pach [SODA'11] that has recently been improved to a OPT^ε-approximation algorithm by Cslovjecsek, Pilipczuk and Węgrzycki [SODA '24], which also extends to an arbitrary set of convex polygons. Our result builds on, and generalizes the recent constant factor approximation algorithms for the maximum independent set of axis-parallel rectangles problem (which is a special case of our problem with d = 2) by Mitchell [FOCS'21] and Gálvez, Khan, Mari, Mömke, Reddy, and Wiese [SODA'22].
Cite as

Fabrizio Grandoni, Edin Husić, Mathieu Mari, and Antoine Tinguely. Approximating the Maximum Independent Set of Convex Polygons with a Bounded Number of Directions. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 61:1-61:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{grandoni_et_al:LIPIcs.SoCG.2024.61,
  author =	{Grandoni, Fabrizio and Husi\'{c}, Edin and Mari, Mathieu and Tinguely, Antoine},
  title =	{{Approximating the Maximum Independent Set of Convex Polygons with a Bounded Number of Directions}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{61:1--61:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.61},
  URN =		{urn:nbn:de:0030-drops-200066},
  doi =		{10.4230/LIPIcs.SoCG.2024.61},
  annote =	{Keywords: Approximation algorithms, packing, independent set, polygons}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.17
FPT Algorithms for Finding Near-Cliques in c-Closed Graphs

Authors: Balaram Behera, Edin Husić, Shweta Jain, Tim Roughgarden, and C. Seshadhri

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
Finding large cliques or cliques missing a few edges is a fundamental algorithmic task in the study of real-world graphs, with applications in community detection, pattern recognition, and clustering. A number of effective backtracking-based heuristics for these problems have emerged from recent empirical work in social network analysis. Given the NP-hardness of variants of clique counting, these results raise a challenge for beyond worst-case analysis of these problems. Inspired by the triadic closure of real-world graphs, Fox et al. (SICOMP 2020) introduced the notion of c-closed graphs and proved that maximal clique enumeration is fixed-parameter tractable with respect to c. In practice, due to noise in data, one wishes to actually discover "near-cliques", which can be characterized as cliques with a sparse subgraph removed. In this work, we prove that many different kinds of maximal near-cliques can be enumerated in polynomial time (and FPT in c) for c-closed graphs. We study various established notions of such substructures, including k-plexes, complements of bounded-degeneracy and bounded-treewidth graphs. Interestingly, our algorithms follow relatively simple backtracking procedures, analogous to what is done in practice. Our results underscore the significance of the c-closed graph class for theoretical understanding of social network analysis.
Cite as

Balaram Behera, Edin Husić, Shweta Jain, Tim Roughgarden, and C. Seshadhri. FPT Algorithms for Finding Near-Cliques in c-Closed Graphs. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 17:1-17:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{behera_et_al:LIPIcs.ITCS.2022.17,
  author =	{Behera, Balaram and Husi\'{c}, Edin and Jain, Shweta and Roughgarden, Tim and Seshadhri, C.},
  title =	{{FPT Algorithms for Finding Near-Cliques in c-Closed Graphs}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{17:1--17:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.17},
  URN =		{urn:nbn:de:0030-drops-156130},
  doi =		{10.4230/LIPIcs.ITCS.2022.17},
  annote =	{Keywords: c-closed graph, dense subgraphs, FPT algorithm, enumeration algorithm, k-plex, Moon-Moser theorem}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.33
Auction Algorithms for Market Equilibrium with Weak Gross Substitute Demands and Their Applications

Authors: Jugal Garg, Edin Husić, and László A. Végh

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
We consider the Arrow-Debreu exchange market model where agents' demands satisfy the weak gross substitutes (WGS) property. This is a well-studied property, in particular, it gives a sufficient condition for the convergence of the classical tâtonnement dynamics. In this paper, we present a simple auction algorithm that obtains an approximate market equilibrium for WGS demands. Such auction algorithms have been previously known for restricted classes of WGS demands only. As an application of our technique, we obtain an efficient algorithm to find an approximate spending-restricted market equilibrium for WGS demands, a model that has been recently introduced as a continuous relaxation of the Nash social welfare (NSW) problem. This leads to a polynomial-time constant factor approximation algorithm for NSW with budget separable piecewise linear utility functions; only a pseudopolynomial approximation algorithm was known for this setting previously.
Cite as

Jugal Garg, Edin Husić, and László A. Végh. Auction Algorithms for Market Equilibrium with Weak Gross Substitute Demands and Their Applications. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{garg_et_al:LIPIcs.STACS.2021.33,
  author =	{Garg, Jugal and Husi\'{c}, Edin and V\'{e}gh, L\'{a}szl\'{o} A.},
  title =	{{Auction Algorithms for Market Equilibrium with Weak Gross Substitute Demands and Their Applications}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{33:1--33:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.33},
  URN =		{urn:nbn:de:0030-drops-136786},
  doi =		{10.4230/LIPIcs.STACS.2021.33},
  annote =	{Keywords: auction algorithm, weak gross substitutes, Fisher equilibrium, Gale equilibrium, Nash social welfare}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2019.21
The Independent Set Problem Is FPT for Even-Hole-Free Graphs

Authors: Edin Husić, Stéphan Thomassé, and Nicolas Trotignon

Published in: LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)

Abstract
The class of even-hole-free graphs is very similar to the class of perfect graphs, and was indeed a cornerstone in the tools leading to the proof of the Strong Perfect Graph Theorem. However, the complexity of computing a maximum independent set (MIS) is a long-standing open question in even-hole-free graphs. From the hardness point of view, MIS is W[1]-hard in the class of graphs without induced 4-cycle (when parameterized by the solution size). Halfway of these, we show in this paper that MIS is FPT when parameterized by the solution size in the class of even-hole-free graphs. The main idea is to apply twice the well-known technique of augmenting graphs to extend some initial independent set.
Cite as

Edin Husić, Stéphan Thomassé, and Nicolas Trotignon. The Independent Set Problem Is FPT for Even-Hole-Free Graphs. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 21:1-21:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{husic_et_al:LIPIcs.IPEC.2019.21,
  author =	{Husi\'{c}, Edin and Thomass\'{e}, St\'{e}phan and Trotignon, Nicolas},
  title =	{{The Independent Set Problem Is FPT for Even-Hole-Free Graphs}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{21:1--21:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Jansen, Bart M. P. and Telle, Jan Arne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.21},
  URN =		{urn:nbn:de:0030-drops-114826},
  doi =		{10.4230/LIPIcs.IPEC.2019.21},
  annote =	{Keywords: independent set, FPT algorithm, even-hole-free graph, augmenting graph}
}
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