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Documents authored by Karpov, Nikolai

Document
DOI: 10.4230/LIPIcs.WABI.2018.22
A Multi-labeled Tree Edit Distance for Comparing "Clonal Trees" of Tumor Progression

Authors: Nikolai Karpov, Salem Malikic, Md. Khaledur Rahman, and S. Cenk Sahinalp

Published in: LIPIcs, Volume 113, 18th International Workshop on Algorithms in Bioinformatics (WABI 2018)

Abstract
We introduce a new edit distance measure between a pair of "clonal trees", each representing the progression and mutational heterogeneity of a tumor sample, constructed by the use of single cell or bulk high throughput sequencing data. In a clonal tree, each vertex represents a specific tumor clone, and is labeled with one or more mutations in a way that each mutation is assigned to the oldest clone that harbors it. Given two clonal trees, our multi-labeled tree edit distance (MLTED) measure is defined as the minimum number of mutation/label deletions, (empty) leaf deletions, and vertex (clonal) expansions, applied in any order, to convert each of the two trees to the maximal common tree. We show that the MLTED measure can be computed efficiently in polynomial time and it captures the similarity between trees of different clonal granularity well. We have implemented our algorithm to compute MLTED exactly and applied it to a variety of data sets successfully. The source code of our method can be found in: https://github.com/khaled-rahman/leafDelTED.
Cite as

Nikolai Karpov, Salem Malikic, Md. Khaledur Rahman, and S. Cenk Sahinalp. A Multi-labeled Tree Edit Distance for Comparing "Clonal Trees" of Tumor Progression. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{karpov_et_al:LIPIcs.WABI.2018.22,
  author =	{Karpov, Nikolai and Malikic, Salem and Rahman, Md. Khaledur and Sahinalp, S. Cenk},
  title =	{{A Multi-labeled Tree Edit Distance for Comparing "Clonal Trees" of Tumor Progression}},
  booktitle =	{18th International Workshop on Algorithms in Bioinformatics (WABI 2018)},
  pages =	{22:1--22:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-082-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{113},
  editor =	{Parida, Laxmi and Ukkonen, Esko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2018.22},
  URN =		{urn:nbn:de:0030-drops-93242},
  doi =		{10.4230/LIPIcs.WABI.2018.22},
  annote =	{Keywords: Intra-tumor heterogeneity, tumor evolution, multi-labeled tree, tree edit distance, dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2017.24
An Exponential Lower Bound for Cut Sparsifiers in Planar Graphs

Authors: Nikolai Karpov, Marcin Pilipczuk, and Anna Zych-Pawlewicz

Published in: LIPIcs, Volume 89, 12th International Symposium on Parameterized and Exact Computation (IPEC 2017)

Abstract
Given an edge-weighted graph G with a set Q of k terminals, a mimicking network is a graph with the same set of terminals that exactly preserves the sizes of minimum cuts between any partition of the terminals. A natural question in the area of graph compression is to provide as small mimicking networks as possible for input graph G being either an arbitrary graph or coming from a specific graph class. In this note we show an exponential lower bound for cut mimicking networks in planar graphs: there are edge-weighted planar graphs with k terminals that require 2^(k-2) edges in any mimicking network. This nearly matches an upper bound of O(k * 2^(2k)) of Krauthgamer and Rika [SODA 2013, arXiv:1702.05951] and is in sharp contrast with the O(k^2) upper bound under the assumption that all terminals lie on a single face [Goranci, Henzinger, Peng, arXiv:1702.01136]. As a side result we show a hard instance for the double-exponential upper bounds given by Hagerup, Katajainen, Nishimura, and Ragde [JCSS 1998], Khan and Raghavendra [IPL 2014], and Chambers and Eppstein [JGAA 2013].
Cite as

Nikolai Karpov, Marcin Pilipczuk, and Anna Zych-Pawlewicz. An Exponential Lower Bound for Cut Sparsifiers in Planar Graphs. In 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 89, pp. 24:1-24:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{karpov_et_al:LIPIcs.IPEC.2017.24,
  author =	{Karpov, Nikolai and Pilipczuk, Marcin and Zych-Pawlewicz, Anna},
  title =	{{An Exponential Lower Bound for Cut Sparsifiers in Planar Graphs}},
  booktitle =	{12th International Symposium on Parameterized and Exact Computation (IPEC 2017)},
  pages =	{24:1--24:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-051-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{89},
  editor =	{Lokshtanov, Daniel and Nishimura, Naomi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2017.24},
  URN =		{urn:nbn:de:0030-drops-85603},
  doi =		{10.4230/LIPIcs.IPEC.2017.24},
  annote =	{Keywords: mimicking networks, planar graphs}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.6
Parameterized Algorithms for Partitioning Graphs into Highly Connected Clusters

Authors: Ivan Bliznets and Nikolai Karpov

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
Clustering is a well-known and important problem with numerous applications. The graph-based model is one of the typical cluster models. In the graph model generally clusters are defined as cliques. However, such approach might be too restrictive as in some applications, not all objects from the same cluster must be connected. That is why different types of cliques relaxations often considered as clusters. In our work, we consider a problem of partitioning graph into clusters and a problem of isolating cluster of a special type where by cluster we mean highly connected subgraph. Initially, such clusterization was proposed by Hartuv and Shamir. And their HCS clustering algorithm was extensively applied in practice. It was used to cluster cDNA fingerprints, to find complexes in protein-protein interaction data, to group protein sequences hierarchically into superfamily and family clusters, to find families of regulatory RNA structures. The HCS algorithm partitions graph in highly connected subgraphs. However, it is achieved by deletion of not necessarily the minimum number of edges. In our work, we try to minimize the number of edge deletions. We consider problems from the parameterized point of view where the main parameter is a number of allowed edge deletions. The presented algorithms significantly improve previous known running times for the Highly Connected Deletion (improved from \cOs\left(81^k\right) to \cOs\left(3^k\right)), Isolated Highly Connected Subgraph (from \cOs(4^k) to \cOs\left(k^{\cO\left(k^{\sfrac{2}{3}}\right)}\right) ), Seeded Highly Connected Edge Deletion (from \cOs\left(16^{k^{\sfrac{3}{4}}}\right) to \cOs\left(k^{\sqrt{k}}\right)) problems. Furthermore, we present a subexponential algorithm for Highly Connected Deletion problem if the number of clusters is bounded. Overall our work contains three subexponential algorithms which is unusual as very recently there were known very few problems admitting subexponential algorithms.
Cite as

Ivan Bliznets and Nikolai Karpov. Parameterized Algorithms for Partitioning Graphs into Highly Connected Clusters. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bliznets_et_al:LIPIcs.MFCS.2017.6,
  author =	{Bliznets, Ivan and Karpov, Nikolai},
  title =	{{Parameterized Algorithms for Partitioning Graphs into Highly Connected Clusters}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.6},
  URN =		{urn:nbn:de:0030-drops-80728},
  doi =		{10.4230/LIPIcs.MFCS.2017.6},
  annote =	{Keywords: clustering, parameterized complexity, highly connected}
}
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