9 Search Results for "Serna, Maria"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.24
Languages of Words of Low Automatic Complexity Are Hard to Compute

Authors: Joey Chen, Bjørn Kjos-Hanssen, Ivan Koswara, Linus Richter, and Frank Stephan

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
The automatic complexity of a finite word (string) is an analogue for finite automata of Sipser’s distinguishing complexity (1983) and was introduced by Shallit and Wang (2001). For a finite alphabet Σ of at least two elements, we consider the non-deterministic automatic complexity given by exactly - yet not necessarily uniquely - accepting automata: a word x ∈ Σ^* has exact non-deterministic automatic complexity k ∈ ℕ if there exists a non-deterministic automaton of k states which accepts x while rejecting every other word of the same length as x, and no automaton of fewer states has this property. Importantly, and in contrast to the classical notion, the witnessing automaton may have multiple paths of computation accepting x. We denote this measure of complexity by A_{Ne}, and study a class of languages of low A_{Ne}-complexity defined as L_q = {x ∈ Σ^* : A_{Ne}(x) < q|x|}, which is parameterised by rationals q ∈ (0,1/2) (generalising a class of sets first studied by Kjos-Hanssen). We show that for every q ∈ (0,1/2), this class is neither context-free nor recognisable by certain Boolean circuits. In the process, we answer an open question of Kjos-Hanssen quantifying the complexity of L_{1/3} in terms of Boolean circuits, and also prove the Shannon effect for A_{Ne}.
Cite as

Joey Chen, Bjørn Kjos-Hanssen, Ivan Koswara, Linus Richter, and Frank Stephan. Languages of Words of Low Automatic Complexity Are Hard to Compute. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.FSTTCS.2025.24,
  author =	{Chen, Joey and Kjos-Hanssen, Bj{\o}rn and Koswara, Ivan and Richter, Linus and Stephan, Frank},
  title =	{{Languages of Words of Low Automatic Complexity Are Hard to Compute}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.24},
  URN =		{urn:nbn:de:0030-drops-251055},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.24},
  annote =	{Keywords: Automatic complexity, automata theory, formal languages, Boolean circuits, Shannon effect}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.34
On the Approximability of Train Routing and the Min-Max Disjoint Paths Problem

Authors: Umang Bhaskar, Katharina Eickhoff, Lennart Kauther, Jannik Matuschke, Britta Peis, and Laura Vargas Koch

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
In train routing, the headway is the minimum distance that must be maintained between successive trains for safety and robustness. We introduce a model for train routing that requires a fixed headway to be maintained between trains, and study the problem of minimizing the makespan, i.e., the arrival time of the last train, in a single-source single-sink network. For this problem, we first show that there exists an optimal solution where trains move in convoys - that is, the optimal paths for any two trains are either the same or are arc-disjoint. Via this insight, we are able to reduce the approximability of our train routing problem to that of the min-max disjoint paths problem, which asks for a collection of disjoint paths where the maximum length of any path in the collection is as small as possible. While min-max disjoint paths inherits a strong inapproximability result on directed acyclic graphs from the multi-level bottleneck assignment problem, we show that a natural greedy composition approach yields a logarithmic approximation in the number of disjoint paths for series-parallel graphs. We also present an alternative analysis of this approach that yields a guarantee depending on how often the decomposition tree of the series-parallel graph alternates between series and parallel compositions on any root-leaf path.
Cite as

Umang Bhaskar, Katharina Eickhoff, Lennart Kauther, Jannik Matuschke, Britta Peis, and Laura Vargas Koch. On the Approximability of Train Routing and the Min-Max Disjoint Paths Problem. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhaskar_et_al:LIPIcs.ESA.2025.34,
  author =	{Bhaskar, Umang and Eickhoff, Katharina and Kauther, Lennart and Matuschke, Jannik and Peis, Britta and Vargas Koch, Laura},
  title =	{{On the Approximability of Train Routing and the Min-Max Disjoint Paths Problem}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.34},
  URN =		{urn:nbn:de:0030-drops-245029},
  doi =		{10.4230/LIPIcs.ESA.2025.34},
  annote =	{Keywords: Train Routing, Scheduling, Approximation Algorithms, Flows over Time, Min-Max Disjoint Paths}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.124
Subgraph Counting in Subquadratic Time for Bounded Degeneracy Graphs

Authors: Daniel Paul-Pena and C. Seshadhri

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study the classic problem of subgraph counting, where we wish to determine the number of occurrences of a fixed pattern graph H in an input graph G of n vertices. Our focus is on bounded degeneracy inputs, a rich family of graph classes that also characterizes real-world massive networks. Building on the seminal techniques introduced by Chiba-Nishizeki (SICOMP 1985), a recent line of work has built subgraph counting algorithms for bounded degeneracy graphs. Assuming fine-grained complexity conjectures, there is a complete characterization of patterns H for which linear time subgraph counting is possible. For every r ≥ 6, there exists an H with r vertices that cannot be counted in linear time. In this paper, we initiate a study of subquadratic algorithms for subgraph counting on bounded degeneracy graphs. We prove that when H has at most 9 vertices, subgraph counting can be done in Õ(n^{5/3}) time. As a secondary result, we give improved algorithms for counting cycles of length at most 10. Previously, no subquadratic algorithms were known for the above problems on bounded degeneracy graphs. Our main conceptual contribution is a framework that reduces subgraph counting in bounded degeneracy graphs to counting smaller hypergraphs in arbitrary graphs. We believe that our results will help build a general theory of subgraph counting for bounded degeneracy graphs.
Cite as

Daniel Paul-Pena and C. Seshadhri. Subgraph Counting in Subquadratic Time for Bounded Degeneracy Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 124:1-124:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{paulpena_et_al:LIPIcs.ICALP.2025.124,
  author =	{Paul-Pena, Daniel and Seshadhri, C.},
  title =	{{Subgraph Counting in Subquadratic Time for Bounded Degeneracy Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{124:1--124:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.124},
  URN =		{urn:nbn:de:0030-drops-235010},
  doi =		{10.4230/LIPIcs.ICALP.2025.124},
  annote =	{Keywords: Homomorphism counting, Bounded degeneracy graphs, Fine-grained complexity, Subgraph counting}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.27
Computing Oriented Spanners and Their Dilation

Authors: Kevin Buchin, Antonia Kalb, Anil Maheshwari, Saeed Odak, Carolin Rehs, Michiel Smid, and Sampson Wong

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Given a point set P in a metric space and a real number t ≥ 1, an oriented t-spanner is an oriented graph G = (P, E), where for every pair of distinct points p and q in P, the shortest oriented closed walk in G that contains p and q is at most a factor t longer than the perimeter of the smallest triangle in P containing p and q. The oriented dilation of a graph G is the minimum t for which G is an oriented t-spanner. For arbitrary point sets of size n in ℝ^d, where d ≥ 2 is a constant, the only known oriented spanner construction is an oriented 2-spanner with binom(n,2) edges. Moreover, there exists a set P of four points in the plane, for which the oriented dilation is larger than 1.46, for any oriented graph on P. We present the first algorithm that computes, in Euclidean space, a sparse oriented spanner whose oriented dilation is bounded by a constant. More specifically, for any set of n points in ℝ^d, where d is a constant, we construct an oriented (2+ε)-spanner with 𝒪(n) edges in 𝒪(n log n) time and 𝒪(n) space. Our construction uses the well-separated pair decomposition and an algorithm that computes a (1+ε)-approximation of the minimum-perimeter triangle in P containing two given query points in 𝒪(log n) time. While our algorithm is based on first computing a suitable undirected graph and then orienting it, we show that, in general, computing the orientation of an undirected graph that minimises its oriented dilation is NP-hard, even for point sets in the Euclidean plane. We further prove that even if the oriented graph is already given, computing its oriented dilation is APSP-hard for points in a general metric space. We complement this result with an algorithm that approximates the oriented dilation of a given graph in subcubic time for point sets in ℝ^d, where d is a constant.
Cite as

Kevin Buchin, Antonia Kalb, Anil Maheshwari, Saeed Odak, Carolin Rehs, Michiel Smid, and Sampson Wong. Computing Oriented Spanners and Their Dilation. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{buchin_et_al:LIPIcs.SoCG.2025.27,
  author =	{Buchin, Kevin and Kalb, Antonia and Maheshwari, Anil and Odak, Saeed and Rehs, Carolin and Smid, Michiel and Wong, Sampson},
  title =	{{Computing Oriented Spanners and Their Dilation}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{27:1--27:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.27},
  URN =		{urn:nbn:de:0030-drops-231792},
  doi =		{10.4230/LIPIcs.SoCG.2025.27},
  annote =	{Keywords: spanner, oriented graph, dilation, orientation, well-separated pair decomposition, minimum-perimeter triangle}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.49
On Sparse Covers of Minor Free Graphs, Low Dimensional Metric Embeddings, and Other Applications

Authors: Arnold Filtser

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Given a metric space (X,d_X), a (β,s,Δ)-sparse cover is a collection of clusters 𝒞 ⊆ P(X) with diameter at most Δ, such that for every point x ∈ X, the ball B_X(x,Δ/β) is fully contained in some cluster C ∈ 𝒞, and x belongs to at most s clusters in 𝒞. Our main contribution is to show that the shortest path metric of every K_r-minor free graphs admits (O(r),O(r²),Δ)-sparse cover, and for every ε > 0, (4+ε,O(1/ε)^r,Δ)-sparse cover (for arbitrary Δ > 0). We then use this sparse cover to show that every K_r-minor free graph embeds into 𝓁_∞^{Õ(1/ε)^{r+1}⋅log n} with distortion 3+ε (resp. into 𝓁_∞^{Õ(r²)⋅log n} with distortion O(r)). Further, among other applications, this sparse cover immediately implies an algorithm for the oblivious buy-at-bulk problem in fixed minor free graphs with the tight approximation factor O(log n) (previously nothing beyond general graphs was known).
Cite as

Arnold Filtser. On Sparse Covers of Minor Free Graphs, Low Dimensional Metric Embeddings, and Other Applications. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 49:1-49:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{filtser:LIPIcs.SoCG.2025.49,
  author =	{Filtser, Arnold},
  title =	{{On Sparse Covers of Minor Free Graphs, Low Dimensional Metric Embeddings, and Other Applications}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{49:1--49:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.49},
  URN =		{urn:nbn:de:0030-drops-232015},
  doi =		{10.4230/LIPIcs.SoCG.2025.49},
  annote =	{Keywords: Sparse cover, minor free graphs, metric embeddings, 𝓁\underline∞, oblivious buy-at-bulk}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.8
Branch Prediction Analysis of Morris-Pratt and Knuth-Morris-Pratt Algorithms

Authors: Cyril Nicaud, Carine Pivoteau, and Stéphane Vialette

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
We investigate the classical Morris-Pratt and Knuth-Morris-Pratt pattern matching algorithms from the perspective of computer architecture, focusing on the effects of incorporating a simple branch prediction mechanism into the computational model. Assuming a fixed pattern and a random text, we derive precise estimates for the number of branch mispredictions incurred by these algorithms when using local predictors. Our analysis relies on tools from automata theory and Markov chains, offering a theoretical framework that can be extended to other text processing algorithms and more sophisticated branch prediction strategies.
Cite as

Cyril Nicaud, Carine Pivoteau, and Stéphane Vialette. Branch Prediction Analysis of Morris-Pratt and Knuth-Morris-Pratt Algorithms. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nicaud_et_al:LIPIcs.CPM.2025.8,
  author =	{Nicaud, Cyril and Pivoteau, Carine and Vialette, St\'{e}phane},
  title =	{{Branch Prediction Analysis of Morris-Pratt and Knuth-Morris-Pratt Algorithms}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.8},
  URN =		{urn:nbn:de:0030-drops-231027},
  doi =		{10.4230/LIPIcs.CPM.2025.8},
  annote =	{Keywords: Pattern matching, branch prediction, transducers, average case complexity, Markov chains}
}
Document
DOI: 10.4230/LIPIcs.SEA.2022.7
Relating Real and Synthetic Social Networks Through Centrality Measures

Authors: Maria J. Blesa, Mihail Eduard Popa, and Maria Serna

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract
We perform here a comparative study on the behaviour of real and synthetic social networks with respect to a selection of nine centrality measures. Some of them are topology based (degree, closeness, betweenness), while others consider the relevance of the actors within the network (Katz, PageRank) or their ability to spread influence through it (Independent Cascade rank, Linear Threshold Rank). We run different experiments on synthetic social networks, with 1K, 10K, and 100K nodes, generated according to the Gaussian Random partition model, the stochastic block model, the LFR benchmark graph model and hyperbolic geometric graphs model. Some real social networks are also considered, with the aim of discovering how do they relate to the synthetic models in terms of centrality. Apart from usual statistical measures, we perform a correlation analysis between all the nine measures. Our results indicate that, in general, the correlation matrices of the different models scale nicely with size. Moreover, the correlation plots distinguish four categories that classify most of the real networks studied here. Those categories have a clear correspondence with particular configurations of the models for synthetic networks.
Cite as

Maria J. Blesa, Mihail Eduard Popa, and Maria Serna. Relating Real and Synthetic Social Networks Through Centrality Measures. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{blesa_et_al:LIPIcs.SEA.2022.7,
  author =	{Blesa, Maria J. and Popa, Mihail Eduard and Serna, Maria},
  title =	{{Relating Real and Synthetic Social Networks Through Centrality Measures}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{7:1--7:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.7},
  URN =		{urn:nbn:de:0030-drops-165410},
  doi =		{10.4230/LIPIcs.SEA.2022.7},
  annote =	{Keywords: centrality measures, influence spread models, synthetic social networks}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.20
Data-Compression for Parametrized Counting Problems on Sparse Graphs

Authors: Eun Jung Kim, Maria Serna, and Dimitrios M. Thilikos

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
We study the concept of compactor, which may be seen as a counting-analogue of kernelization in counting parameterized complexity. For a function F:Sigma^* -> N and a parameterization kappa: Sigma^* -> N, a compactor (P,M) consists of a polynomial-time computable function P, called condenser, and a computable function M, called extractor, such that F=M o P, and the condensing P(x) of x has length at most s(kappa(x)), for any input x in Sigma^*. If s is a polynomial function, then the compactor is said to be of polynomial-size. Although the study on counting-analogue of kernelization is not unprecedented, it has received little attention so far. We study a family of vertex-certified counting problems on graphs that are MSOL-expressible; that is, for an MSOL-formula phi with one free set variable to be interpreted as a vertex subset, we want to count all A subseteq V(G) where |A|=k and (G,A) models phi. In this paper, we prove that every vertex-certified counting problems on graphs that is MSOL-expressible and treewidth modulable, when parameterized by k, admits a polynomial-size compactor on H-topological-minor-free graphs with condensing time O(k^2n^2) and decoding time 2^{O(k)}. This implies the existence of an FPT-algorithm of running time O(n^2 k^2)+2^{O(k)}. All aforementioned complexities are under the Uniform Cost Measure (UCM) model where numbers can be stored in constant space and arithmetic operations can be done in constant time.
Cite as

Eun Jung Kim, Maria Serna, and Dimitrios M. Thilikos. Data-Compression for Parametrized Counting Problems on Sparse Graphs. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 20:1-20:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kim_et_al:LIPIcs.ISAAC.2018.20,
  author =	{Kim, Eun Jung and Serna, Maria and Thilikos, Dimitrios M.},
  title =	{{Data-Compression for Parametrized Counting Problems on Sparse Graphs}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{20:1--20:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.20},
  URN =		{urn:nbn:de:0030-drops-99688},
  doi =		{10.4230/LIPIcs.ISAAC.2018.20},
  annote =	{Keywords: Parameterized counting, compactor, protrusion decomposition}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.630
Absorption Time of the Moran Process

Authors: Josep Díaz, Leslie Ann Goldberg, David Richerby, and Maria Serna

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
The Moran process models the spread of mutations in populations on graphs. We investigate the absorption time of the process, which is the time taken for a mutation introduced at a randomly chosen vertex to either spread to the whole population, or to become extinct. It is known that the expected absorption time for an advantageous mutation is polynomial on an n-vertex undirected graph, which allows the behaviour of the process on undirected graphs to be analysed using the Markov chain Monte Carlo method. We show that this does not extend to directed graphs by exhibiting an infinite family of directed graphs for which the expected absorption time is exponential in the number of vertices. However, for regular directed graphs, we give the expected absorption time is blog n lower bound and an explicit quadratic upper bound. We exhibit families of graphs matching these bounds and give improved bounds for other families of graphs, based on isoperimetric number. Our results are obtained via stochastic dominations which we demonstrate by establishing a coupling in a related continuous-time model. The coupling also implies several natural domination results regarding the fixation probability of the original (discrete-time) process, resolving a conjecture of Shakarian, Roos and Johnson.
Cite as

Josep Díaz, Leslie Ann Goldberg, David Richerby, and Maria Serna. Absorption Time of the Moran Process. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 630-642, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{diaz_et_al:LIPIcs.APPROX-RANDOM.2014.630,
  author =	{D{\'\i}az, Josep and Goldberg, Leslie Ann and Richerby, David and Serna, Maria},
  title =	{{Absorption Time of the Moran Process}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{630--642},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.630},
  URN =		{urn:nbn:de:0030-drops-47279},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.630},
  annote =	{Keywords: Moran Process}
}
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