IA Scholar Query: An LP-rounding 2√2-approximation for restricted maximum acyclic subgraph.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgMon, 05 Dec 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Observational and Interventional Causal Learning for Regret-Minimizing Control
https://scholar.archive.org/work/syk7bpenmraxzj7r742c6k76oe
We explore how observational and interventional causal discovery methods can be combined. A state-of-the-art observational causal discovery algorithm for time series capable of handling latent confounders and contemporaneous effects, called LPCMCI, is extended to profit from casual constraints found through randomized control trials. Numerical results show that, given perfect interventional constraints, the reconstructed structural causal models (SCMs) of the extended LPCMCI allow 84.6% of the time for the optimal prediction of the target variable. The implementation of interventional and observational causal discovery is modular, allowing causal constraints from other sources. The second part of this thesis investigates the question of regret minimizing control by simultaneously learning a causal model and planning actions through the causal model. The idea is that an agent to optimize a measured variable first learns the system's mechanics through observational causal discovery. The agent then intervenes on the most promising variable with randomized values allowing for the exploitation and generation of new interventional data. The agent then uses the interventional data to enhance the causal model further, allowing improved actions the next time. The extended LPCMCI can be favorable compared to the original LPCMCI algorithm. The numerical results show that detecting and using interventional constraints leads to reconstructed SCMs that allow 60.9% of the time for the optimal prediction of the target variable in contrast to the baseline of 53.6% when using the original LPCMCI algorithm. Furthermore, the induced average regret decreases from 1.2 when using the original LPCMCI algorithm to 1.0 when using the extended LPCMCI algorithm with interventional discovery.Christian Reiserwork_syk7bpenmraxzj7r742c6k76oeMon, 05 Dec 2022 00:00:00 GMTAttacking Shortest Paths by Cutting Edges
https://scholar.archive.org/work/nrndkyze35fspj45nzxbfpoxgq
Identifying shortest paths between nodes in a network is a common graph analysis problem that is important for many applications involving routing of resources. An adversary that can manipulate the graph structure could alter traffic patterns to gain some benefit (e.g., make more money by directing traffic to a toll road). This paper presents the Force Path Cut problem, in which an adversary removes edges from a graph to make a particular path the shortest between its terminal nodes. We prove that this problem is APX-hard, but introduce PATHATTACK, a polynomial-time approximation algorithm that guarantees a solution within a logarithmic factor of the optimal value. In addition, we introduce the Force Edge Cut and Force Node Cut problems, in which the adversary targets a particular edge or node, respectively, rather than an entire path. We derive a nonconvex optimization formulation for these problems, and derive a heuristic algorithm that uses PATHATTACK as a subroutine. We demonstrate all of these algorithms on a diverse set of real and synthetic networks, illustrating the network types that benefit most from the proposed algorithms.Benjamin A. Miller and Zohair Shafi and Wheeler Ruml and Yevgeniy Vorobeychik and Tina Eliassi-Rad and Scott Alfeldwork_nrndkyze35fspj45nzxbfpoxgqMon, 21 Nov 2022 00:00:00 GMTCheeger Inequalities for Directed Graphs and Hypergraphs Using Reweighted Eigenvalues
https://scholar.archive.org/work/lj2kaskxd5hqlgoechfrgst2mq
We derive Cheeger inequalities for directed graphs and hypergraphs using the reweighted eigenvalue approach that was recently developed for vertex expansion in undirected graphs [OZ22,KLT22,JPV22]. The goal is to develop a new spectral theory for directed graphs and an alternative spectral theory for hypergraphs. The first main result is a Cheeger inequality relating the vertex expansion ψ⃗(G) of a directed graph G to the vertex-capacitated maximum reweighted second eigenvalue λ⃗_2^v*: λ⃗_2^v*≲ψ⃗(G) ≲√(λ⃗_2^v*·log (Δ/λ⃗_2^v*)). This provides a combinatorial characterization of the fastest mixing time of a directed graph by vertex expansion, and builds a new connection between reweighted eigenvalued, vertex expansion, and fastest mixing time for directed graphs. The second main result is a stronger Cheeger inequality relating the edge conductance ϕ⃗(G) of a directed graph G to the edge-capacitated maximum reweighted second eigenvalue λ⃗_2^e*: λ⃗_2^e*≲ϕ⃗(G) ≲√(λ⃗_2^e*·log (1/λ⃗_2^e*)). This provides a certificate for a directed graph to be an expander and a spectral algorithm to find a sparse cut in a directed graph, playing a similar role as Cheeger's inequality in certifying graph expansion and in the spectral partitioning algorithm for undirected graphs. We also use this reweighted eigenvalue approach to derive the improved Cheeger inequality for directed graphs, and furthermore to derive several Cheeger inequalities for hypergraphs that match and improve the existing results in [Lou15,CLTZ18]. These are supporting results that this provides a unifying approach to lift the spectral theory for undirected graphs to more general settings.Lap Chi Lau, Kam Chuen Tung, Robert Wangwork_lj2kaskxd5hqlgoechfrgst2mqThu, 17 Nov 2022 00:00:00 GMTOn Constrained Mixed-Integer DR-Submodular Minimization
https://scholar.archive.org/work/lvmh4octxjdz3k2z24ml7tjecu
DR-submodular functions encompass a broad class of functions which are generally non-convex and non-concave. We study the problem of minimizing any DR-submodular function, with continuous and general integer variables, under box constraints and possibly additional monotonicity constraints. We propose valid linear inequalities for the epigraph of any DR-submodular function under the constraints. We further provide the complete convex hull of such an epigraph, which, surprisingly, turns out to be polyhedral. We propose a polynomial-time exact separation algorithm for our proposed valid inequalities, with which we first establish the polynomial-time solvability of this class of mixed-integer nonlinear optimization problems.Qimeng Yu, Simge Küçükyavuzwork_lvmh4octxjdz3k2z24ml7tjecuMon, 14 Nov 2022 00:00:00 GMTSoftware Systems Implementation and Domain-Specific Architectures towards Graph Analytics
https://scholar.archive.org/work/a7gcksxyczfibcelliuyyfrxme
Graph analytics, which mainly includes graph processing, graph mining, and graph learning, has become increasingly important in several domains, including social network analysis, bioinformatics, and machine learning. However, graph analytics applications suffer from poor locality, limited bandwidth, and low parallelism owing to the irregular sparse structure, explosive growth, and dependencies of graph data. To address those challenges, several programming models, execution modes, and messaging strategies are proposed to improve the utilization of traditional hardware and performance. In recent years, novel computing and memory devices have emerged, e.g., HMCs, HBM, and ReRAM, providing massive bandwidth and parallelism resources, making it possible to address bottlenecks in graph applications. To facilitate understanding of the graph analytics domain, our study summarizes and categorizes current software systems implementation and domain-specific architectures. Finally, we discuss the future challenges of graph analytics.Hai Jin, Hao Qi, Jin Zhao, Xinyu Jiang, Yu Huang, Chuangyi Gui, Qinggang Wang, Xinyang Shen, Yi Zhang, Ao Hu, Dan Chen, Chaoqiang Liu, Haifeng Liu, Haiheng He, Xiangyu Ye, Runze Wang, Jingrui Yuan, Pengcheng Yao, Yu Zhang, Long Zheng, Xiaofei Liaowork_a7gcksxyczfibcelliuyyfrxmeSat, 29 Oct 2022 00:00:00 GMTSocial Choice for Social Good: Proposals for Democratic Innovation from Computer Science
https://scholar.archive.org/work/bkhftvqgbjabpjqzjni4g5fdli
Driven by shortcomings of current democratic systems, practitioners and political scientists are exploring democratic innovations, i.e., institutions for decision-making that more directly involve constituents. In this thesis, we support this exploration using tools from computer science, via three approaches: we design practical algorithms for use in democratic innovations, we mathematically analyze the fairness properties of proposed decision-making processes, and we identify extensions of such processes that satisfy desirable properties. Our work mixes techniques from computational social choice, algorithms, optimization, probabilistic modeling, and empirical analysis. In Part I, we apply the frst two approaches to citizens' assemblies, which are randomly selected panels of constituents who deliberate on a policy issue. We analyze existing algorithms for the random selection of these assemblies, and we design new algorithms for this task that are provably fair and now widely used in practice. In addition, we design algorithms for partitioning assembly members into deliberation groups, which allow more members to interact than before. Part II identifes extensions to liquid democracy and legislative apportionment. First, we demonstrate that a variant of liquid democracy, in which agents are asked for two potential delegates rather than a single delegate, reduces the concentration of power observed in classic liquid democracy. Second, we extend legislative elections over parties to approval ballots, and give apportionment methods for this setting that satisfy strong proportionality axioms. Finally, we extend a proposal for the randomized apportionment of legislative seats over states to satisfy additional monotonicity axioms. In Part III of this thesis, we engage with a specifc policy topic, refugee resettlement. We design algorithms for allocating resettled refugees to localities in a country, which improves these refugees' chances of fnding [...]Paul Goelzwork_bkhftvqgbjabpjqzjni4g5fdliMon, 24 Oct 2022 00:00:00 GMTA Differentiable Relaxation of Graph Segmentation and Alignment for AMR Parsing
https://scholar.archive.org/work/r4z466osjzb3vl4q7ef7rd7lka
Meaning Representations (AMR) are a broad-coverage semantic formalism which represents sentence meaning as a directed acyclic graph. To train most AMR parsers, one needs to segment the graph into subgraphs and align each such subgraph to a word in a sentence; this is normally done at preprocessing, relying on hand-crafted rules. In contrast, we treat both alignment and segmentation as latent variables in our model and induce them as part of end-to-end training. As marginalizing over the structured latent variables is infeasible, we use the variational autoencoding framework. To ensure end-to-end differentiable optimization, we introduce a differentiable relaxation of the segmentation and alignment problems. We observe that inducing segmentation yields substantial gains over using a 'greedy' segmentation heuristic. The performance of our method also approaches that of a model that relies on the segmentation rules of , which were hand-crafted to handle individual AMR constructions.Chunchuan Lyu, Shay B. Cohen, Ivan Titovwork_r4z466osjzb3vl4q7ef7rd7lkaMon, 24 Oct 2022 00:00:00 GMTLocally Restricted Proof Labeling Schemes
https://scholar.archive.org/work/rm7qfs2d6vaoddmk6zannjzkvi
Introduced by Korman, Kutten, and Peleg (PODC 2005), a proof labeling scheme (PLS) is a distributed verification system dedicated to evaluating if a given configured graph satisfies a certain property. It involves a centralized prover, whose role is to provide proof that a given configured graph is a yes-instance by means of assigning labels to the nodes, and a distributed verifier, whose role is to verify the validity of the given proof via local access to the assigned labels. In this paper, we introduce the notion of a locally restricted PLS in which the prover's power is restricted to that of a LOCAL algorithm with a polylogarithmic number of rounds. To circumvent inherent impossibilities of PLSs in the locally restricted setting, we turn to models that relax the correctness requirements by allowing the verifier to accept some no-instances as long as they are not "too far" from satisfying the property in question. To this end, we evaluate (1) distributed graph optimization problems (OptDGPs) based on the notion of an approximate proof labeling scheme (APLS) (analogous to the type of relaxation used in sequential approximation algorithms); and (2) configured graph families (CGFs) based on the notion of a testing proof labeling schemes (TPLS) (analogous to the type of relaxation used in property testing algorithms). The main contribution of the paper comes in the form of two generic compilers, one for OptDGPs and one for CGFs: given a black-box access to an APLS (resp., PLS) for a large class of OptDGPs (resp., CGFs), the compiler produces a locally restricted APLS (resp., TPLS) for the same problem, while losing at most a (1 + ε) factor in the scheme's relaxation guarantee. An appealing feature of the two compilers is that they only require a logarithmic additive label size overhead.Yuval Emek, Yuval Gil, Shay Kutten, Christian Scheidelerwork_rm7qfs2d6vaoddmk6zannjzkviMon, 17 Oct 2022 00:00:00 GMTStreaming and Matching Problems with Submodular Functions
https://scholar.archive.org/work/pqhn4636xnhl7foze3yc6bxpjq
Faculté informatique et communications Laboratoire de théorie du calcul 2 Programme doctoral en informatique et communicationsParitosh Gargwork_pqhn4636xnhl7foze3yc6bxpjqMon, 17 Oct 2022 00:00:00 GMTNotes on CSPs and Polymorphisms
https://scholar.archive.org/work/kouwgol6o5h55lxjkqyjupnv2i
These are notes from a multi-year learning seminar on the algebraic approach to Constraint Satisfaction Problems (CSPs). The main topics covered are the theory of algebraic structures with few subpowers, the theory of absorbing subalgebras and its applications to studying CSP templates which can be solved by local consistency methods, and the dichotomy theorem for conservative CSP templates. Subsections and appendices cover supplementary material.Zarathustra Bradywork_kouwgol6o5h55lxjkqyjupnv2iThu, 13 Oct 2022 00:00:00 GMTGrowing a Random Maximal Independent Set Produces a 2-approximate Vertex Cover
https://scholar.archive.org/work/jyw6pr75xvawnm6qbjtlnfevpm
This paper presents a fast and simple new 2-approximation algorithm for minimum weighted vertex cover. The unweighted version of this algorithm is equivalent to a well-known greedy maximal independent set algorithm. We prove that this independent set algorithm produces a 2-approximate vertex cover, and we provide a principled new way to generalize it to node-weighted graphs. Our analysis is inspired by connections to a clustering objective called correlation clustering. To demonstrate the relationship between these problems, we show how a simple Pivot algorithm for correlation clustering implicitly approximates a special type of hypergraph vertex cover problem. Finally, we use implicit implementations of this maximal independent set algorithm to develop fast and simple 2-approximation algorithms for certain edge-deletion problems that can be reduced to vertex cover in an approximation preserving way.Nate Veldtwork_jyw6pr75xvawnm6qbjtlnfevpmSat, 10 Sep 2022 00:00:00 GMTOASIcs, Volume 106, ATMOS 2022, Complete Volume
https://scholar.archive.org/work/k3l2xowdkvfxdelwxhf2xrcp6y
OASIcs, Volume 106, ATMOS 2022, Complete VolumeMattia D'Emidio, Niels Lindnerwork_k3l2xowdkvfxdelwxhf2xrcp6yTue, 06 Sep 2022 00:00:00 GMTKochen-Specker Contextuality
https://scholar.archive.org/work/vub2wqx3bnfvhfcecbkbdcbkku
A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here, compatible measurements are those that can be implemented simultaneously, or more generally, those who are jointly measurable. This conflict is generically called quantum contextuality. In this article, we present an introduction to this subject and its current status. We review several proofs of the Kochen-Specker theorem and different notions of contextuality. We explain how to experimentally test some of these notions and discuss connections between contextuality and nonlocality or graph theory. Finally, we review some applications of contextuality in quantum information processing.Costantino Budroni, Adán Cabello, Otfried Gühne, Matthias Kleinmann, Jan-Åke Larssonwork_vub2wqx3bnfvhfcecbkbdcbkkuWed, 31 Aug 2022 00:00:00 GMTFitting Metrics and Ultrametrics with Minimum Disagreements
https://scholar.archive.org/work/7zgl4rvk5bgspa5cer3izquik4
Given x ∈ (ℝ_≥ 0)^[n]2 recording pairwise distances, the METRIC VIOLATION DISTANCE (MVD) problem asks to compute the ℓ_0 distance between x and the metric cone; i.e., modify the minimum number of entries of x to make it a metric. Due to its large number of applications in various data analysis and optimization tasks, this problem has been actively studied recently. We present an O(log n)-approximation algorithm for MVD, exponentially improving the previous best approximation ratio of O(OPT^1/3) of Fan et al. [ SODA, 2018]. Furthermore, a major strength of our algorithm is its simplicity and running time. We also study the related problem of ULTRAMETRIC VIOLATION DISTANCE (UMVD), where the goal is to compute the ℓ_0 distance to the cone of ultrametrics, and achieve a constant factor approximation algorithm. The UMVD can be regarded as an extension of the problem of fitting ultrametrics studied by Ailon and Charikar [SIAM J. Computing, 2011] and by Cohen-Addad et al. [FOCS, 2021] from ℓ_1 norm to ℓ_0 norm. We show that this problem can be favorably interpreted as an instance of Correlation Clustering with an additional hierarchical structure, which we solve using a new O(1)-approximation algorithm for correlation clustering that has the structural property that it outputs a refinement of the optimum clusters. An algorithm satisfying such a property can be considered of independent interest. We also provide an O(log n loglog n) approximation algorithm for weighted instances. Finally, we investigate the complementary version of these problems where one aims at choosing a maximum number of entries of x forming an (ultra-)metric. In stark contrast with the minimization versions, we prove that these maximization versions are hard to approximate within any constant factor assuming the Unique Games Conjecture.Vincent Cohen-Addad, Chenglin Fan, Euiwoong Lee, Arnaud de Mesmaywork_7zgl4rvk5bgspa5cer3izquik4Mon, 29 Aug 2022 00:00:00 GMTLifted edges as connectivity priors for multicut and disjoint paths
https://scholar.archive.org/work/edizj43isvflhhihrsapdwjlhu
This work studies graph decompositions and their representation by 0/1 labeling of edges. We study two problems. The first is multicut (MC) which represents decompositions of undirected graphs (clustering of nodes into connected components). The second is disjoint paths (DP) in directed acyclic graphs where the clusters correspond to nodedisjoint paths. Unlike an alternative representation by node labeling, the number of clusters is not part of the input but is fully determined by the costs of edges. I would like to thank all my co-authors for a pleasant and constructive cooperation. Besides my supervisor Paul Swoboda, I would like to name especially Roberto Henschel, Timo Kaiser, Bjoern Andres, and Jan-Hendrik Lange for their major contribution to the shared publications that are part of this thesis. The publications could not be realized without their part of the work. I would like to thank Bjoern Andres for his supervision and help during the work on our common paper. I would like to mention also Michal Rolinek who helped us with our latest publication. I would like to thank Jiles Vreeken, Marcel Schulz and Markus List who cooperated with me on a research project that is not part of this thesis. I am very grateful to Bernt Schiele, the director of our department, who provided me with good working conditions, fully supported me in combining my working duties with family, and found a solution in the difficult stage of my PhD study by finding a new supervisor. Also, other people at MPI and Saarland University helped me to organize my work and family life and helped me with administrative issues.Andrea Hornakova, Universität Des Saarlandeswork_edizj43isvflhhihrsapdwjlhuMon, 29 Aug 2022 00:00:00 GMTLocally Restricted Proof Labeling Schemes (Full Version)
https://scholar.archive.org/work/b6pyhqafevgn5iwtl74j6wsuxi
Introduced by Korman, Kutten, and Peleg (PODC 2005), a proof labeling scheme (PLS) is a distributed verification system dedicated to evaluating if a given configured graph satisfies a certain property. It involves a centralized prover, whose role is to provide proof that a given configured graph is a yes-instance by means of assigning labels to the nodes, and a distributed verifier, whose role is to verify the validity of the given proof via local access to the assigned labels. In this paper, we introduce the notion of a locally restricted PLS in which the prover's power is restricted to that of a LOCAL algorithm with a polylogarithmic number of rounds. To circumvent inherent impossibilities of PLSs in the locally restricted setting, we turn to models that relax the correctness requirements by allowing the verifier to accept some no-instances as long as they are not "too far" from satisfying the property in question. To this end, we evaluate (1) distributed graph optimization problems (OptDGPs) based on the notion of an approximate proof labeling scheme (APLS) (analogous to the type of relaxation used in sequential approximation algorithms); and (2) configured graph families (CGFs) based on the notion of atesting proof labeling schemes (TPLS) (analogous to the type of relaxation used in property testing algorithms).Yuval Emek, Yuval Gil, Shay Kuttenwork_b6pyhqafevgn5iwtl74j6wsuxiWed, 24 Aug 2022 00:00:00 GMTHaplotype-aware variant selection for genome graphs
https://scholar.archive.org/work/t2ldsseybbeqzb2m7cfzpp3uni
Graph-based genome representations have proven to be a powerful tool in genomic analysis due to their ability to encode variations found in multiple haplotypes and capture population genetic diversity. Such graphs also unavoidably contain paths which switch between haplotypes (i.e., recombinant paths) and thus do not fully match any of the constituent haplotypes. The number of such recombinant paths increases combinatorially with path length and cause inefficiencies an d fa lse po sitives wh en ma pping re ads. In this paper, we study the problem of finding reduced haplotypeaware genome graphs that incorporate only a selected subset of variants, yet contain paths corresponding to all 𝛼-long substrings of the input haplotypes (i.e., non-recombinant paths) with at most 𝛿 mismatches. Solving this problem optimally, i.e., minimizing the number of variants selected, is previously known to be NP-hard [14] . Here, we first establish several inapproximability results regarding finding haplotype-aware reduced variation graphs of optimal size. We then present an integer linear programming (ILP) formulation for solving the problem, and experimentally demonstrate this is a computationally feasible approach for real-world problems and provides far superior reduction compared to prior approaches.Neda Tavakoli, Daniel Gibney, Srinivas Aluruwork_t2ldsseybbeqzb2m7cfzpp3uniSun, 07 Aug 2022 00:00:00 GMTMaximizing Fair Content Spread via Edge Suggestion in Social Networks
https://scholar.archive.org/work/g3q3qqxhdrh7fbnaky7u637oby
Content spread inequity is a potential unfairness issue in online social networks, disparately impacting minority groups. In this paper, we view friendship suggestion, a common feature in social network platforms, as an opportunity to achieve an equitable spread of content. In particular, we propose to suggest a subset of potential edges (currently not existing in the network but likely to be accepted) that maximizes content spread while achieving fairness. Instead of re-engineering the existing systems, our proposal builds a fairness wrapper on top of the existing friendship suggestion components. We prove the problem is NP-hard and inapproximable in polynomial time unless P = NP. Therefore, allowing relaxation of the fairness constraint, we propose an algorithm based on LP-relaxation and randomized rounding with fixed approximation ratios on fairness and content spread. We provide multiple optimizations, further improving the performance of our algorithm in practice. Besides, we propose a scalable algorithm that dynamically adds subsets of nodes, chosen via iterative sampling, and solves smaller problems corresponding to these nodes. Besides theoretical analysis, we conduct comprehensive experiments on real and synthetic data sets. Across different settings, our algorithms found solutions with nearzero unfairness while significantly increasing the content spread. Our scalable algorithm could process a graph with half a million nodes on a single machine, reducing the unfairness to around 0.0004 while lifting content spread by 43%.Ian P. Swift, Sana Ebrahimi, Azade Nova, Abolfazl Asudehwork_g3q3qqxhdrh7fbnaky7u637obySat, 06 Aug 2022 00:00:00 GMTQuantum Computing: Lecture Notes
https://scholar.archive.org/work/2pcfo6u7jzg25alp6mv6fq3w2y
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in subsequent years. The first 10 chapters cover the circuit model and the main quantum algorithms (Deutsch-Jozsa, Simon, Shor, Hidden Subgroup Problem, Grover, quantum walks, Hamiltonian simulation and HHL). They are followed by 3 chapters about complexity, 4 chapters about distributed ("Alice and Bob") settings, a chapter about quantum machine learning, and a final chapter about quantum error correction. Appendices A and B give a brief introduction to the required linear algebra and some other mathematical and computer science background. All chapters come with exercises, with some hints provided in Appendix C.Ronald de Wolfwork_2pcfo6u7jzg25alp6mv6fq3w2yTue, 02 Aug 2022 00:00:00 GMTVertex Deletion Parameterized by Elimination Distance and Even Less
https://scholar.archive.org/work/sdzr3cd7lrdmnjd5v32mha6lde
We study the parameterized complexity of various classic vertex-deletion problems such as Odd cycle transversal, Vertex planarization, and Chordal vertex deletion under hybrid parameterizations. Existing FPT algorithms for these problems either focus on the parameterization by solution size, detecting solutions of size k in time f(k) · n^O(1), or width parameterizations, finding arbitrarily large optimal solutions in time f(w) · n^O(1) for some width measure w like treewidth. We unify these lines of research by presenting FPT algorithms for parameterizations that can simultaneously be arbitrarily much smaller than the solution size and the treewidth. We consider two classes of parameterizations which are relaxations of either treedepth of treewidth. They are related to graph decompositions in which subgraphs that belong to a target class H (e.g., bipartite or planar) are considered simple. First, we present a framework for computing approximately optimal decompositions for miscellaneous classes H. Namely, if the cost of an optimal decomposition is k, we show how to find a decomposition of cost k^O(1) in time f(k) · n^O(1). This is applicable to any graph class H for which the corresponding vertex-deletion problem admits a constant-factor approximation algorithm or an FPT algorithm paramaterized by the solution size. Secondly, we exploit the constructed decompositions for solving vertex-deletion problems by extending ideas from algorithms using iterative compression and the finite state property. For the three mentioned vertex-deletion problems, and all problems which can be formulated as hitting a finite set of connected forbidden (a) minors or (b) (induced) subgraphs, we obtain FPT algorithms with respect to both studied parameterizations.Bart M. P. Jansen, Jari J. H. de Kroon, Michał Włodarczykwork_sdzr3cd7lrdmnjd5v32mha6ldeMon, 18 Jul 2022 00:00:00 GMT