17 Search Results for "Chen, Yijia"

Document
DOI: 10.4230/LIPIcs.STACS.2026.25
Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing

Authors: Marek Černý and Tim Seppelt

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Two graphs G and H are homomorphism indistinguishable over a graph class ℱ if they admit the same number of homomorphisms from every graph F ∈ ℱ. Many graph isomorphism relaxations such as (quantum) isomorphism and cospectrality can be characterised as homomorphism indistinguishability over specific graph classes. Thereby, the problems HomInd(ℱ) of deciding homomorphism indistinguishability over ℱ subsume diverse graph isomorphism relaxations whose complexities range from logspace to undecidable. Establishing the first general result on the complexity of HomInd(ℱ), Seppelt (MFCS 2024) showed that HomInd(ℱ) is in randomised polynomial time for every graph class ℱ of bounded treewidth that can be defined in counting monadic second-order logic CMSO₂. We show that this algorithm is conditionally optimal, i.e. it cannot be derandomised unless polynomial identity testing is in P. For CMSO₂-definable graph classes ℱ of bounded pathwidth, we improve the previous complexity upper bound for HomInd(ℱ) from P to C_ = L and show that this is tight. Secondarily, we establish a connection between homomorphism indistinguishability and multiplicity automata equivalence which allows us to pinpoint the complexity of the latter problem as C_ = L-complete.
Cite as

Marek Černý and Tim Seppelt. Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cerny_et_al:LIPIcs.STACS.2026.25,
  author =	{\v{C}ern\'{y}, Marek and Seppelt, Tim},
  title =	{{Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.25},
  URN =		{urn:nbn:de:0030-drops-255144},
  doi =		{10.4230/LIPIcs.STACS.2026.25},
  annote =	{Keywords: treewidth, Courcelle’s theorem, logspace, multiplicity automata, polynomial identity testing}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.80
FPT Approximations for Connected Maximum Coverage

Authors: Tanmay Inamdar, Satyabrata Jana, Madhumita Kundu, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We revisit connectivity-constrained coverage through a unifying model, Partial Connected Red-Blue Dominating Set (PartialConRBDS). Given a bipartite graph G = (R∪ B,E) with red vertices R and blue vertices B, an auxiliary connectivity graph G_{conn} on R, and integers k,t, the task is to find a set S ⊆ R with |S| ≤ k such that G_{conn}[S] is connected and S dominates at least t blue vertices. This formulation captures connected variants of Maximum Coverage [Hochbaum-Rao, Inf. Proc. Lett., 2020; D'Angelo-Delfaraz, AAMAS 2025], Partial Vertex Cover, and Partial Dominating Set [Khuller et al., SODA 2014; Lamprou et al., TCS 2021] via standard encodings. Limits to parameterized tractability. PartialConRBDS is W[1]-hard parameterized by k even under strong restrictions: it remains hard when G_{conn} is a clique or a star and the incidence graph G is 3-degenerate, or when G is K_{2,2}-free. Inapproximability. For every ε > 0, there is no polynomial-time (1, 1-1/e+ε)-approximation unless 𝖯 = NP. Moreover, under ETH, no algorithm running in f(k)⋅ n^{o(k)} time achieves an g(k)-approximation for k for any computable function g(⋅), or for any ε > 0, a (1-1/e+ε)-approximation for t. Graphical special cases. Partial Connected Dominating Set is W[2]-hard parameterized by k and inherits the same ETH-based f(k)⋅ n^{o(k)} inapproximability bound as above; Partial Connected Vertex Cover is W[1]-hard parameterized by k. These hardness boundaries delineate a natural "sweet spot" for study: within appropriate structural restrictions on the incidence graph, one can still aim for fine-grained (FPT) approximations. Our algorithms. We solve PartialConRBDS exactly by reducing it to Relaxed Directed Steiner Out-Tree in time (2e)^t ⋅ n^{𝒪(1)}. For biclique-free incidences (i.e., when G excludes K_{d,d} as an induced subgraph), we obtain two complementary parameterized schemes: - An Efficient Parameterized Approximation Scheme (EPAS) running in time 2^{𝒪(k² d/ε)}⋅ n^{𝒪(1)} that either returns a connected solution of size at most k covering at least (1-ε)t blue vertices, or correctly reports that no connected size-k solution covers t; and - A Parameterized Approximation Scheme (PAS) running in time 2^{𝒪(kd(k²+log d))}⋅ n^{𝒪(1/ε)} that either returns a connected solution of size at most (1+ε)k covering at least t blue vertices, or correctly reports that no connected size-k solution covers t. Together, these results chart the boundary between hardness and FPT-approximability for connectivity-constrained coverage.
Cite as

Tanmay Inamdar, Satyabrata Jana, Madhumita Kundu, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi. FPT Approximations for Connected Maximum Coverage. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 80:1-80:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{inamdar_et_al:LIPIcs.ITCS.2026.80,
  author =	{Inamdar, Tanmay and Jana, Satyabrata and Kundu, Madhumita and Lokshtanov, Daniel and Saurabh, Saket and Zehavi, Meirav},
  title =	{{FPT Approximations for Connected Maximum Coverage}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{80:1--80:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.80},
  URN =		{urn:nbn:de:0030-drops-253674},
  doi =		{10.4230/LIPIcs.ITCS.2026.80},
  annote =	{Keywords: Partial Dominating Set, Connectivity, Maximum Coverage, FPT Approximation, Fixed-parameter Tractability}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.27
Uniformity Within Parameterized Circuit Classes

Authors: Steef Hegeman, Jan Martens, and Alfons Laarman

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
We study uniformity conditions for parameterized Boolean circuit families. Uniformity conditions require that the infinitely many circuits in a circuit family are in some sense easy to construct from one shared description. For shallow circuit families, logtime-uniformity is often desired but quite technical to prove. Despite that, proving it is often left as an exercise for the reader - even for recently introduced classes in parameterized circuit complexity, where uniformity conditions have not yet been explicitly studied. We formally define parameterized versions of linear-uniformity, logtime-uniformity, and FO-uniformity, and prove that these result in equivalent complexity classes when imposed on para-AC⁰ and para-AC^{0↑}. Overall, we provide a convenient way to verify uniformity for shallow parameterized circuit classes, and thereby substantiate claims of uniformity in the literature.
Cite as

Steef Hegeman, Jan Martens, and Alfons Laarman. Uniformity Within Parameterized Circuit Classes. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hegeman_et_al:LIPIcs.IPEC.2025.27,
  author =	{Hegeman, Steef and Martens, Jan and Laarman, Alfons},
  title =	{{Uniformity Within Parameterized Circuit Classes}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{27:1--27:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.27},
  URN =		{urn:nbn:de:0030-drops-251598},
  doi =		{10.4230/LIPIcs.IPEC.2025.27},
  annote =	{Keywords: Parameterized complexity, circuit complexity, uniformity, descriptive complexity}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.24
A Note on the Parameterised Complexity of Coverability in Vector Addition Systems

Authors: Michał Pilipczuk, Sylvain Schmitz, and Henry Sinclair-Banks

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
We investigate the parameterised complexity of the classic coverability problem for vector addition systems (VAS): V ⊆ ℤ^d, an initial configuration s ∈ ℕ^d, and a target configuration t ∈ ℕ^d, decide whether starting from s, one can iteratively add vectors from V to ultimately arrive at a configuration that is larger than or equal to t on every coordinate, while not observing any negative value on any coordinate along the way. We consider two natural parameters for the problem: the dimension d and the size of V, defined as the total bitsize of its encoding. We present several results charting the complexity of those two parameterisations, among which the highlight is that coverability for VAS parameterised by the dimension and with all the numbers in the input encoded in unary is complete for the class XNL under PL-reductions. We also discuss open problems in the topic, most notably the question about fixed-parameter tractability for the parameterisation by the size of V.
Cite as

Michał Pilipczuk, Sylvain Schmitz, and Henry Sinclair-Banks. A Note on the Parameterised Complexity of Coverability in Vector Addition Systems. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pilipczuk_et_al:LIPIcs.IPEC.2025.24,
  author =	{Pilipczuk, Micha{\l} and Schmitz, Sylvain and Sinclair-Banks, Henry},
  title =	{{A Note on the Parameterised Complexity of Coverability in Vector Addition Systems}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.24},
  URN =		{urn:nbn:de:0030-drops-251563},
  doi =		{10.4230/LIPIcs.IPEC.2025.24},
  annote =	{Keywords: vector addition system, Petri net, parameterised complexity, coverability}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.23
Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes

Authors: Archit Chauhan, Samir Datta, and M. Praveen

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

Abstract
Constructing a Depth First Search (DFS) tree is a fundamental graph problem, whose parallel complexity is still not settled. Reif showed parallel intractability of lex-first DFS. In contrast, randomized parallel algorithms (and more recently, deterministic quasipolynomial parallel algorithms) are known for constructing a DFS tree in general (di)graphs. However a deterministic parallel algorithm for DFS in general graphs remains an elusive goal. Working towards this, a series of works gave deterministic NC algorithms for DFS in planar graphs and digraphs. We further extend these results to more general graph classes, by providing NC algorithms for (di)graphs of bounded genus, and for undirected H-minor-free graphs where H is a fixed graph with at most one crossing. For the case of (di)graphs of bounded treewidth, we further improve the complexity to a Logspace bound. Constructing a maximal path is a simpler problem (that reduces to DFS) for which no deterministic parallel bounds are known for general graphs. For planar graphs a bound of O(log n) parallel time on a CRCW PRAM (thus in NC²) is known. We improve this bound to Logspace.
Cite as

Archit Chauhan, Samir Datta, and M. Praveen. Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes. 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. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chauhan_et_al:LIPIcs.FSTTCS.2025.23,
  author =	{Chauhan, Archit and Datta, Samir and Praveen, M.},
  title =	{{Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{23:1--23:21},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-251041},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.23},
  annote =	{Keywords: Parallel Complexity, Graph Algorithms, Depth First Search, Maximal Path, Planar Graphs, Minor-Free, Treewidth, Logspace}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.34
Adaptive Query Algorithms for Relational Structures Based on Homomorphism Counts

Authors: Balder ten Cate, Phokion G. Kolaitis, and Arnar Á. Kristjánsson

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
A query algorithm based on homomorphism counts is a procedure to decide membership for a class of finite relational structures using only homomorphism count queries. A left query algorithm can ask the number of homomorphisms from any structure to the input structure and a right query algorithm can ask the number of homomorphisms from the input structure to any other structure. We systematically compare the expressive power of different types of left or right query algorithms, including non-adaptive query algorithms, adaptive query algorithms that can ask a bounded number of queries, and adaptive query algorithms that can ask an unbounded number of queries. We also consider query algorithms where the homomorphism counting is done over the Boolean semiring 𝔹, meaning that only the existence of a homomorphism is recorded, not the precise number of them.
Cite as

Balder ten Cate, Phokion G. Kolaitis, and Arnar Á. Kristjánsson. Adaptive Query Algorithms for Relational Structures Based on Homomorphism Counts. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 34:1-34:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tencate_et_al:LIPIcs.MFCS.2025.34,
  author =	{ten Cate, Balder and Kolaitis, Phokion G. and Kristj\'{a}nsson, Arnar \'{A}.},
  title =	{{Adaptive Query Algorithms for Relational Structures Based on Homomorphism Counts}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{34:1--34:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.34},
  URN =		{urn:nbn:de:0030-drops-241413},
  doi =		{10.4230/LIPIcs.MFCS.2025.34},
  annote =	{Keywords: Query algorithms, homomorphisms, homomorphism counts, directed graphs, relational structures, Datalog, constraint satisfaction}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.39
Sampling with a Black Box: Faster Parameterized Approximation Algorithms for Vertex Deletion Problems

Authors: Barış Can Esmer and Ariel Kulik

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

Abstract
In this paper, we present Sampling with a Black Box, a unified framework for the design of parameterized approximation algorithms for vertex deletion problems (e.g., Vertex Cover, Feedback Vertex Set, etc.). The framework relies on two components: - A Sampling Step. A polynomial-time randomized algorithm that, given a graph G, returns a random vertex v such that the optimum of G⧵ {v} is smaller by 1 than the optimum of G, with some prescribed probability q. We show that such algorithms exist for multiple vertex deletion problems. - A Black Box algorithm which is either an exact parameterized algorithm, a polynomial-time approximation algorithm, or a parameterized-approximation algorithm. The framework combines these two components together. The sampling step is applied iteratively to remove vertices from the input graph, and then the solution is extended using the black box algorithm. The process is repeated sufficiently many times so that the target approximation ratio is attained with a constant probability. We use the technique to derive parameterized approximation algorithms for several vertex deletion problems, including Feedback Vertex Set, d-Hitting Set and 𝓁-Path Vertex Cover. In particular, for every approximation ratio 1 < β < 2, we attain a parameterized β-approximation for Feedback Vertex Set, which is faster than the parameterized β-approximation of [Jana, Lokshtanov, Mandal, Rai and Saurabh, MFCS 23']. Furthermore, our algorithms are always faster than the algorithms attained using Fidelity Preserving Transformations [Fellows, Kulik, Rosamond, and Shachnai, JCSS 18'].
Cite as

Barış Can Esmer and Ariel Kulik. Sampling with a Black Box: Faster Parameterized Approximation Algorithms for Vertex Deletion Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{canesmer_et_al:LIPIcs.ICALP.2025.39,
  author =	{Can Esmer, Bar{\i}\c{s} and Kulik, Ariel},
  title =	{{Sampling with a Black Box: Faster Parameterized Approximation Algorithms for Vertex Deletion Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{39:1--39:20},
  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.2025.39},
  URN =		{urn:nbn:de:0030-drops-234165},
  doi =		{10.4230/LIPIcs.ICALP.2025.39},
  annote =	{Keywords: Parameterized Approximation Algorithms, Random Sampling}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.17
Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths

Authors: Matthias Bentert, Fedor V. Fomin, and Petr A. Golovach

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We examine the possibility of approximating Maximum Vertex-Disjoint Shortest Paths. In this problem, the input is an edge-weighted (directed or undirected) n-vertex graph G along with k terminal pairs (s_1,t_1),(s_2,t_2),…,(s_k,t_k). The task is to connect as many terminal pairs as possible by pairwise vertex-disjoint paths such that each path is a shortest path between the respective terminals. Our work is anchored in the recent breakthrough by Lochet [SODA '21], which demonstrates the polynomial-time solvability of the problem for a fixed value of k. Lochet’s result implies the existence of a polynomial-time ck-approximation for Maximum Vertex-Disjoint Shortest Paths, where c ≤ 1 is a constant. (One can guess 1/c terminal pairs to connect in k^O(1/c) time and then utilize Lochet’s algorithm to compute the solution in n^f(1/c) time.) Our first result suggests that this approximation algorithm is, in a sense, the best we can hope for. More precisely, assuming the gap-ETH, we exclude the existence of an o(k)-approximation within f(k) ⋅ poly(n) time for any function f that only depends on k. Our second result demonstrates the infeasibility of achieving an approximation ratio of m^{1/2-ε} in polynomial time, unless P = NP. It is not difficult to show that a greedy algorithm selecting a path with the minimum number of arcs results in a ⌈√𝓁⌉-approximation, where 𝓁 is the number of edges in all the paths of an optimal solution. Since 𝓁 ≤ n, this underscores the tightness of the m^{1/2-ε}-inapproximability bound. Additionally, we establish that Maximum Vertex-Disjoint Shortest Paths is fixed-parameter tractable when parameterized by 𝓁 but does not admit a polynomial kernel. Our hardness results hold for undirected graphs with unit weights, while our positive results extend to scenarios where the input graph is directed and features arbitrary (non-negative) edge weights.
Cite as

Matthias Bentert, Fedor V. Fomin, and Petr A. Golovach. Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bentert_et_al:LIPIcs.STACS.2025.17,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Golovach, Petr A.},
  title =	{{Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.17},
  URN =		{urn:nbn:de:0030-drops-228422},
  doi =		{10.4230/LIPIcs.STACS.2025.17},
  annote =	{Keywords: Inapproximability, Fixed-parameter tractability, Parameterized approximation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.65
On Average Baby PIH and Its Applications

Authors: Yuwei Liu, Yijia Chen, Shuangle Li, Bingkai Lin, and Xin Zheng

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
The Parameterized Inapproximability Hypothesis (PIH) asserts that no FPT algorithm can decide whether a given 2CSP instance parameterized by the number of variables is satisfiable, or at most a constant fraction of its constraints can be satisfied simultaneously. In a recent breakthrough, Guruswami, Lin, Ren, Sun, and Wu (STOC 2024) proved the PIH under the Exponential Time Hypothesis (ETH). However, it remains a major open problem whether the PIH can be established assuming only W[1]≠FPT. Towards this goal, Guruswami, Ren, and Sandeep (CCC 2024) showed a weaker version of the PIH called the Baby PIH under W[1]≠FPT. In addition, they proposed one more intermediate assumption known as the Average Baby PIH, which might lead to further progress on the PIH. As the main contribution of this paper, we prove that the Average Baby PIH holds assuming W[1]≠FPT. Given a 2CSP instance where the number of its variables is the parameter, the Average Baby PIH states that no FPT algorithm can decide whether (i) it is satisfiable or (ii) any multi-assignment that satisfies all constraints must assign each variable more than r values on average for any fixed constant r > 1. So there is a gap between (i) and (ii) on the average number of values that are assigned to a variable, i.e., 1 vs. r. If this gap occurs in each variable instead of on average, we get the original Baby PIH. So central to our paper is an FPT self-reduction for 2CSP instances that turns the above gap for each variable into a gap on average. By the known W[1]-hardness for the Baby PIH, this proves that the Average Baby PIH holds under W[1] ≠ FPT. As applications, we obtain (i) for the first time, the W[1]-hardness of constant approximating k-ExactCover, and (ii) a tight relationship between running time lower bounds in the Average Baby PIH and approximating the parameterized Nearest Codeword Problem (k-NCP).
Cite as

Yuwei Liu, Yijia Chen, Shuangle Li, Bingkai Lin, and Xin Zheng. On Average Baby PIH and Its Applications. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 65:1-65:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{liu_et_al:LIPIcs.STACS.2025.65,
  author =	{Liu, Yuwei and Chen, Yijia and Li, Shuangle and Lin, Bingkai and Zheng, Xin},
  title =	{{On Average Baby PIH and Its Applications}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{65:1--65:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.65},
  URN =		{urn:nbn:de:0030-drops-228900},
  doi =		{10.4230/LIPIcs.STACS.2025.65},
  annote =	{Keywords: Average Baby PIH, Parameterized Inapproximability, Constraint Satisfaction Problem, Exact Set Cover, W\lbrack1\rbrack-hardness}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.58
The Computational Complexity of Factored Graphs

Authors: Shreya Gupta, Boyang Huang, Russell Impagliazzo, Stanley Woo, and Christopher Ye

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct representation. An efficient algorithm (with respect to the compressed input size) could then lead to more efficient computations than algorithms taking the explicit, uncompressed object as input. This leads to a natural question: when does knowing the input instance has a more succinct representation make computation easier? We initiate the study of the computational complexity of problems on factored graphs: graphs that are given as a formula of products and unions on smaller graphs. For any graph problem, we define a parameterized version that takes factored graphs as input, parameterized by the number of (smaller) ordinary graphs used to construct the factored graph. In this setting, we characterize the parameterized complexity of several natural graph problems, exhibiting a variety of complexities. We show that a decision version of lexicographically first maximal independent set is XP-complete, and therefore unconditionally not fixed-parameter tractable (FPT). On the other hand, we show that clique counting is FPT. Finally, we show that reachability is XNL-complete. Moreover, XNL is contained in FPT if and only if NL is contained in some fixed polynomial time.
Cite as

Shreya Gupta, Boyang Huang, Russell Impagliazzo, Stanley Woo, and Christopher Ye. The Computational Complexity of Factored Graphs. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 58:1-58:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gupta_et_al:LIPIcs.ITCS.2025.58,
  author =	{Gupta, Shreya and Huang, Boyang and Impagliazzo, Russell and Woo, Stanley and Ye, Christopher},
  title =	{{The Computational Complexity of Factored Graphs}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{58:1--58:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.58},
  URN =		{urn:nbn:de:0030-drops-226865},
  doi =		{10.4230/LIPIcs.ITCS.2025.58},
  annote =	{Keywords: Parameterized Complexity, Fine-grained complexity, Fixed-parameter tractability, Graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.32
On Algorithms Based on Finitely Many Homomorphism Counts

Authors: Yijia Chen, Jörg Flum, Mingjun Liu, and Zhiyang Xun

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

Abstract
It is well known [L. Lovász, 1967] that up to isomorphism a graph G is determined by the homomorphism counts hom(F, G), i.e., by the number of homomorphisms from F to G where F ranges over all graphs. Moreover, it suffices that F ranges over the graphs with at most as many vertices as G. Thus, in principle, we can answer any query concerning G with only accessing the hom(⋅, G)’s instead of G itself. In this paper, we deal with queries for which there is a hom algorithm, i.e., there are finitely many graphs F₁, …, F_k such that for any graph G whether it is a Yes-instance of the query is already determined by the vector hom^⟶_{F₁, …, F_k}(G): = (hom(F₁, G), …, hom(F_k, G)). We observe that planarity of graphs and 3-colorability of graphs, properties expressible in monadic second-order logic, have no hom algorithm. On the other hand, queries expressible as a Boolean combination of universal sentences in first-order logic FO have a hom algorithm. Even though it is not easy to find FO definable queries without a hom algorithm, we succeed to show this for the non-existence of an isolated vertex, a property expressible by the FO sentence ∀ x∃ y Exy, somehow the "simplest" graph property not definable by a Boolean combination of universal sentences. These results provide a characterization of the prefix classes of first-order logic with the property that each query definable by a sentence of the prefix class has a hom algorithm. For adaptive hom algorithms, i.e., algorithms that might access a hom(F_{i+1}, G) with F_{i+1} depending on hom(F_j, G) for 1 ≤ j ≤ i we show that three homomorphism counts hom(⋅, G) are sufficient and in general necessary to determine the (isomorphism type of) G. In particular, by three adaptive queries we can answer any question on G. Moreover, adaptively accessing two hom(⋅, G)’s is already enough to detect an isolated vertex. In 1993 Chaudhuri and Vardi [S. Chaudhuri and M. Y. Vardi, 1993] showed the analogue of the Lovász Isomorphism Theorem for the right homomorphism vector of a graph G, i.e, the vector of values hom(G,F) where F ranges over all graphs characterizes the isomorphism type of G. We study to what extent our results carry over to the right homomorphism vector.
Cite as

Yijia Chen, Jörg Flum, Mingjun Liu, and Zhiyang Xun. On Algorithms Based on Finitely Many Homomorphism Counts. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 32:1-32:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chen_et_al:LIPIcs.MFCS.2022.32,
  author =	{Chen, Yijia and Flum, J\"{o}rg and Liu, Mingjun and Xun, Zhiyang},
  title =	{{On Algorithms Based on Finitely Many Homomorphism Counts}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{32:1--32:15},
  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},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.32},
  URN =		{urn:nbn:de:0030-drops-168301},
  doi =		{10.4230/LIPIcs.MFCS.2022.32},
  annote =	{Keywords: homomorphism numbers, hom algorithms, adaptive hom algorithms}
}
Document
DOI: 10.4230/LIPIcs.CSL.2020.15
FO-Definability of Shrub-Depth

Authors: Yijia Chen and Jörg Flum

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

Abstract
Shrub-depth is a graph invariant often considered as an extension of tree-depth to dense graphs. We show that the model-checking problem of monadic second-order logic on a class of graphs of bounded shrub-depth can be decided by AC^0-circuits after a precomputation on the formula. This generalizes a similar result on graphs of bounded tree-depth [Y. Chen and J. Flum, 2018]. At the core of our proof is the definability in first-order logic of tree-models for graphs of bounded shrub-depth.
Cite as

Yijia Chen and Jörg Flum. FO-Definability of Shrub-Depth. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chen_et_al:LIPIcs.CSL.2020.15,
  author =	{Chen, Yijia and Flum, J\"{o}rg},
  title =	{{FO-Definability of Shrub-Depth}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.15},
  URN =		{urn:nbn:de:0030-drops-116587},
  doi =		{10.4230/LIPIcs.CSL.2020.15},
  annote =	{Keywords: shrub-depth, model-checking, monadic second-order logic}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.54
The Complexity of Homomorphism Indistinguishability

Authors: Jan Böker, Yijia Chen, Martin Grohe, and Gaurav Rattan

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
For every graph class {F}, let HomInd({F}) be the problem of deciding whether two given graphs are homomorphism-indistinguishable over {F}, i.e., for every graph F in {F}, the number hom(F, G) of homomorphisms from F to G equals the corresponding number hom(F, H) for H. For several natural graph classes (such as paths, trees, bounded treewidth graphs), homomorphism-indistinguishability over the class has an efficient structural characterization, resulting in polynomial time solvability [H. Dell et al., 2018]. In particular, it is known that two non-isomorphic graphs are homomorphism-indistinguishable over the class {T}_k of graphs of treewidth k if and only if they are not distinguished by k-dimensional Weisfeiler-Leman algorithm, a central heuristic for isomorphism testing: this characterization implies a polynomial time algorithm for HomInd({T}_k), for every fixed k in N. In this paper, we show that there is a polynomial-time-decidable class {F} of undirected graphs of bounded treewidth such that HomInd({F}) is undecidable. Our second hardness result concerns the class {K} of complete graphs. We show that HomInd({K}) is co-NP-hard, and in fact, we show completeness for the class C_=P (under P-time Turing reductions). On the algorithmic side, we show that HomInd({P}) can be solved in polynomial time for the class {P} of directed paths. We end with a brief study of two variants of the HomInd({F}) problem: (a) the problem of lexographic-comparison of homomorphism numbers of two graphs, and (b) the problem of computing certain distance-measures (defined via homomorphism numbers) between two graphs.
Cite as

Jan Böker, Yijia Chen, Martin Grohe, and Gaurav Rattan. The Complexity of Homomorphism Indistinguishability. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 54:1-54:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{boker_et_al:LIPIcs.MFCS.2019.54,
  author =	{B\"{o}ker, Jan and Chen, Yijia and Grohe, Martin and Rattan, Gaurav},
  title =	{{The Complexity of Homomorphism Indistinguishability}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{54:1--54:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.54},
  URN =		{urn:nbn:de:0030-drops-109980},
  doi =		{10.4230/LIPIcs.MFCS.2019.54},
  annote =	{Keywords: graph homomorphism numbers, counting complexity, treewidth}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.84
Short Proofs Are Hard to Find

Authors: Ian Mertz, Toniann Pitassi, and Yuanhao Wei

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We obtain a streamlined proof of an important result by Alekhnovich and Razborov [Michael Alekhnovich and Alexander A. Razborov, 2008], showing that it is hard to automatize both tree-like and general Resolution. Under a different assumption than [Michael Alekhnovich and Alexander A. Razborov, 2008], our simplified proof gives improved bounds: we show under ETH that these proof systems are not automatizable in time n^f(n), whenever f(n) = o(log^{1/7 - epsilon} log n) for any epsilon > 0. Previously non-automatizability was only known for f(n) = O(1). Our proof also extends fairly straightforwardly to prove similar hardness results for PCR and Res(r).
Cite as

Ian Mertz, Toniann Pitassi, and Yuanhao Wei. Short Proofs Are Hard to Find. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 84:1-84:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{mertz_et_al:LIPIcs.ICALP.2019.84,
  author =	{Mertz, Ian and Pitassi, Toniann and Wei, Yuanhao},
  title =	{{Short Proofs Are Hard to Find}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{84:1--84:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.84},
  URN =		{urn:nbn:de:0030-drops-106605},
  doi =		{10.4230/LIPIcs.ICALP.2019.84},
  annote =	{Keywords: automatizability, Resolution, SAT solvers, proof complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.26
Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices

Authors: Pavel Dvořák, Andreas Emil Feldmann, Dušan Knop, Tomáš Masařík, Tomáš Toufar, and Pavel Veselý

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
We study the Steiner Tree problem, in which a set of terminal vertices needs to be connected in the cheapest possible way in an edge-weighted graph. This problem has been extensively studied from the viewpoint of approximation and also parametrization. In particular, on one hand Steiner Tree is known to be APX-hard, and W[2]-hard on the other, if parameterized by the number of non-terminals (Steiner vertices) in the optimum solution. In contrast to this we give an efficient parameterized approximation scheme (EPAS), which circumvents both hardness results. Moreover, our methods imply the existence of a polynomial size approximate kernelization scheme (PSAKS) for the considered parameter. We further study the parameterized approximability of other variants of Steiner Tree, such as Directed Steiner Tree and Steiner Forest. For neither of these an EPAS is likely to exist for the studied parameter: for Steiner Forest an easy observation shows that the problem is APX-hard, even if the input graph contains no Steiner vertices. For Directed Steiner Tree we prove that computing a constant approximation for this parameter is W[1]-hard. Nevertheless, we show that an EPAS exists for Unweighted Directed Steiner Tree. Also we prove that there is an EPAS and a PSAKS for Steiner Forest if in addition to the number of Steiner vertices, the number of connected components of an optimal solution is considered to be a parameter.
Cite as

Pavel Dvořák, Andreas Emil Feldmann, Dušan Knop, Tomáš Masařík, Tomáš Toufar, and Pavel Veselý. Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dvorak_et_al:LIPIcs.STACS.2018.26,
  author =	{Dvo\v{r}\'{a}k, Pavel and Feldmann, Andreas Emil and Knop, Du\v{s}an and Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Toufar, Tom\'{a}\v{s} and Vesel\'{y}, Pavel},
  title =	{{Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{26:1--26:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.26},
  URN =		{urn:nbn:de:0030-drops-85158},
  doi =		{10.4230/LIPIcs.STACS.2018.26},
  annote =	{Keywords: Steiner Tree, Steiner Forest, Approximation Algorithms, Parameterized Algorithms, Lossy Kernelization}
}
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