IA Scholar Query: Efficient Enumeration of Maximal k-Degenerate Subgraphs in a Chordal Graph.
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Internet Archive Scholar query results feedeninfo@archive.orgThu, 01 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Enumerating Minimal Connected Dominating Sets
https://scholar.archive.org/work/xog6x7yt5ngefmk47hl6kinnrm
The question to enumerate all (inclusion-wise) minimal connected dominating sets in a graph of order n in time significantly less than 2ⁿ is an open question that was asked in many places. We answer this question affirmatively, by providing an enumeration algorithm that runs in time 𝒪(1.9896ⁿ), using polynomial space only. The key to this result is the consideration of this enumeration problem on 2-degenerate graphs, which is proven to be possible in time 𝒪(1.9767ⁿ). Apart from solving this old open question, we also show new lower bound results. More precisely, we construct a family of graphs of order n with Ω(1.4890ⁿ) many minimal connected dominating sets, while previous examples achieved Ω(1.4422ⁿ). Our example happens to yield 4-degenerate graphs. Additionally, we give lower bounds for the previously not considered classes of 2-degenerate and of 3-degenerate graphs, which are Ω(1.3195ⁿ) and Ω(1.4723ⁿ), respectively. We also address essential questions concerning output-sensitive enumeration. Namely, we give reasons why our algorithm cannot be turned into an enumeration algorithm that guarantees polynomial delay without much efforts. More precisely, we prove that it is NP-complete to decide, given a graph G and a vertex set U, if there exists a minimal connected dominating set D with U ⊆ D, even if G is known to be 2-degenerate. Our reduction also shows that even any subexponential delay is not easy to achieve for enumerating minimal connected dominating sets. Another reduction shows that no FPT-algorithms can be expected for this extension problem concerning minimal connected dominating sets, parameterized by |U|. This also adds one more problem to the still rather few natural parameterized problems that are complete for the class W[3]. We also relate our enumeration problem to the famous open Hitting Set Transversal problem, which can be phrased in our context as the question to enumerate all minimal dominating sets of a graph with polynomial delay by showing that a polynomial-delay enumeration algorithm [...]Faisal N. Abu-Khzam, Henning Fernau, Benjamin Gras, Mathieu Liedloff, Kevin Mann, Shiri Chechik, Gonzalo Navarro, Eva Rotenberg, Grzegorz Hermanwork_xog6x7yt5ngefmk47hl6kinnrmThu, 01 Sep 2022 00:00:00 GMTLIPIcs, Volume 240, COSIT 2022, Complete Volume
https://scholar.archive.org/work/7m7bfxazsra63myunecp6u6qgm
LIPIcs, Volume 240, COSIT 2022, Complete VolumeToru Ishikawa, Sara Irina Fabrikant, Stephan Winterwork_7m7bfxazsra63myunecp6u6qgmMon, 22 Aug 2022 00:00:00 GMTOn the Representation of Causal Background Knowledge and its Applications in Causal Inference
https://scholar.archive.org/work/yixfgxqftbgm3ha6qteu3cc4be
Causal background knowledge about the existence or the absence of causal edges and paths is frequently encountered in observational studies. The shared directed edges and links of a subclass of Markov equivalent DAGs refined due to background knowledge can be represented by a causal maximally partially directed acyclic graph (MPDAG). In this paper, we first provide a sound and complete graphical characterization of causal MPDAGs and give a minimal representation of a causal MPDAG. Then, we introduce a novel representation called direct causal clause (DCC) to represent all types of causal background knowledge in a unified form. Using DCCs, we study the consistency and equivalency of causal background knowledge and show that any causal background knowledge set can be equivalently decomposed into a causal MPDAG plus a minimal residual set of DCCs. Polynomial-time algorithms are also provided for checking the consistency, equivalency, and finding the decomposed MPDAG and residual DCCs. Finally, with causal background knowledge, we prove a sufficient and necessary condition to identify causal effects and surprisingly find that the identifiability of causal effects only depends on the decomposed MPDAG. We also develop a local IDA-type algorithm to estimate the possible values of an unidentifiable effect. Simulations suggest that causal background knowledge can significantly improve the identifiability of causal effects.Zhuangyan Fang, Ruiqi Zhao, Yue Liu, Yangbo Hework_yixfgxqftbgm3ha6qteu3cc4beSun, 10 Jul 2022 00:00:00 GMTProceedings of the 2022 Joint Workshop of the German Research Training Groups in Computer Science
https://scholar.archive.org/work/lvykkw5kcfhlvolc6paa2sxczu
Having spent two successive years running online to prevent the spread of the Corona virus, the traditional annual meeting of the German Research Training Groups (RTGs) funded by the Deutsche Forschungsgemeinschaft (DFG) in the field of computer science returns to Schloss Dagstuhl --– Leibniz Center for Informatics, one of the world's premier venues for computer science-related seminars. Returning to Dagstuhl and hosting this meeting as an in-person-only event was a deliberate decision to revive interaction modes that many of the funded researchers had yet to experience: fostering personal interchange of ideas and experiences in order to strengthen the connection within the German computer science community. This volume documents the abstracts of the research topics of funded researchers in the participating RTGs. The event was jointly organized by RTG 2475 (Cybercrime and Forensic Computing) and RTG 2428 (ConVeY --- Continuous Verification of Cyber-Physical Systems). It took place between Sunday, June 12 and Wednesday, June 15, 2022, as in-person only Dagstuhl Event 22243. The meeting featured the usual sequence of research presentations by funded researchers, networking meetings for PIs and RTG coordinators, as well as two invited talks, one by Professor Martina Seidl (JKU Linz, Austria) on "Competitions as Scientific Method" and another by Professor Jennifer Byrne (School of Medical Sciences, The University of Sydney, Australia) titled "An introduction to research paper mills". Because last year's event marked the 25th anniversary of the workshop series, it featured a live interview with Professor Otto Spaniol who had initiated the workshop series in 1996. We document the interview in this volume.Felix Freiling, Helmut Seidl, 2022 2022 Joint Workshop Of The German Research Training Groups In Computer Science June 12–June 15work_lvykkw5kcfhlvolc6paa2sxczuTue, 17 May 2022 00:00:00 GMTEnumerating Connected Dominating Sets
https://scholar.archive.org/work/s7wqpaldxfdv7ghvy3ebs72dde
The question to enumerate all inclusion-minimal connected dominating sets in a graph of order n in time significantly less than 2^n is an open question that was asked in many places. We answer this question affirmatively, by providing an enumeration algorithm that runs in time 𝒪(1.9896^n), using polynomial space only. The key to this result is the consideration of this enumeration problem on 2-degenerate graphs, which is proven to be possible in time 𝒪(1.9767^n). We also show new lower bound results by constructing a family of graphs of order n with Ω(1.4890^n) minimal connected dominating sets, while previous examples achieved Ω(1.4422^n). Our construction results in lower bounds for a few special graph classes. We also address essential questions concerning output-sensitive enumeration. Namely, we give reasons why our algorithm cannot be turned into an enumeration algorithm that guarantees polynomial delay without much efforts. More precisely, we prove that it is NP-complete to decide, given a graph G and a vertex set U, if there exists a minimal connected dominating set D with U⊆ D, even if G is known to be 2-degenerate. Our reduction also shows that even any subexponential delay is not easy to achieve for enumerating minimal connected dominating sets. Another reduction shows that no FPT-algorithms can be expected for this extension problem concerning minimal connected dominating sets, parameterized by |U|. We also relate our enumeration problem to the famous open Hitting Set Transversal problem, which can be phrased in our context as the question to enumerate all minimal dominating sets of a graph with polynomial delay by showing that a polynomial-delay enumeration algorithm for minimal connected dominating sets implies an affirmative algorithmic solution to the Hitting Set Transversal problem.Faisal Abu-Khzam, Henning Fernau, Benjamin Gras, Mathieu Liedloff, Kevin Mannwork_s7wqpaldxfdv7ghvy3ebs72ddeFri, 29 Apr 2022 00:00:00 GMT1-Extendability of independent sets
https://scholar.archive.org/work/x3z2hywlebe2bckdpjjg6zmcwi
In the 70s, Berge introduced 1-extendable graphs (also called B-graphs), which are graphs where every vertex belongs to a maximum independent set. Motivated by an application in the design of wireless networks, we study the computational complexity of 1-extendability, the problem of deciding whether a graph is 1-extendable. We show that, in general, 1-extendability cannot be solved in 2^o(n) time assuming the Exponential Time Hypothesis, where n is the number of vertices of the input graph, and that it remains NP-hard in subcubic planar graphs and in unit disk graphs (which is a natural model for wireless networks). Although 1-extendability seems to be very close to the problem of finding an independent set of maximum size (a.k.a. Maximum Independent Set), we show that, interestingly, there exist 1-extendable graphs for which Maximum Independent Set is NP-hard. Finally, we investigate a parameterized version of 1-extendability.Pierre Bergé, Anthony Busson, Carl Feghali, Rémi Watrigantwork_x3z2hywlebe2bckdpjjg6zmcwiTue, 12 Apr 2022 00:00:00 GMTTwin-width VIII: delineation and win-wins
https://scholar.archive.org/work/pquptnv6a5ehjcpi2e4py2nxx4
We introduce the notion of delineation. A graph class 𝒞 is said delineated if for every hereditary closure 𝒟 of a subclass of 𝒞, it holds that 𝒟 has bounded twin-width if and only if 𝒟 is monadically dependent. An effective strengthening of delineation for a class 𝒞 implies that tractable FO model checking on 𝒞 is perfectly understood: On hereditary closures 𝒟 of subclasses of 𝒞, FO model checking is fixed-parameter tractable (FPT) exactly when 𝒟 has bounded twin-width. Ordered graphs [BGOdMSTT, STOC '22] and permutation graphs [BKTW, JACM '22] are effectively delineated, while subcubic graphs are not. On the one hand, we prove that interval graphs, and even, rooted directed path graphs are delineated. On the other hand, we show that segment graphs, directed path graphs, and visibility graphs of simple polygons are not delineated. In an effort to draw the delineation frontier between interval graphs (that are delineated) and axis-parallel two-lengthed segment graphs (that are not), we investigate the twin-width of restricted segment intersection classes. It was known that (triangle-free) pure axis-parallel unit segment graphs have unbounded twin-width [BGKTW, SODA '21]. We show that K_t,t-free segment graphs, and axis-parallel H_t-free unit segment graphs have bounded twin-width, where H_t is the half-graph or ladder of height t. In contrast, axis-parallel H_4-free two-lengthed segment graphs have unbounded twin-width. Our new results, combined with the known FPT algorithm for FO model checking on graphs given with O(1)-sequences, lead to win-win arguments. For instance, we derive FPT algorithms for k-Ladder on visibility graphs of 1.5D terrains, and k-Independent Set on visibility graphs of simple polygons.Édouard Bonnet, Dibyayan Chakraborty, Eun Jung Kim, Noleen Köhler, Raul Lopes, Stéphan Thomasséwork_pquptnv6a5ehjcpi2e4py2nxx4Fri, 01 Apr 2022 00:00:00 GMTFPT Algorithms for Finding Near-Cliques in c-Closed Graphs
https://scholar.archive.org/work/a2rfbxa52jcoln4i3j2f7o42om
Finding large cliques or cliques missing a few edges is a fundamental algorithmic task in the study of real-world graphs, with applications in community detection, pattern recognition, and clustering. A number of effective backtracking-based heuristics for these problems have emerged from recent empirical work in social network analysis. Given the NP-hardness of variants of clique counting, these results raise a challenge for beyond worst-case analysis of these problems. Inspired by the triadic closure of real-world graphs, Fox et al. (SICOMP 2020) introduced the notion of c-closed graphs and proved that maximal clique enumeration is fixed-parameter tractable with respect to c. In practice, due to noise in data, one wishes to actually discover "near-cliques", which can be characterized as cliques with a sparse subgraph removed. In this work, we prove that many different kinds of maximal near-cliques can be enumerated in polynomial time (and FPT in c) for c-closed graphs. We study various established notions of such substructures, including k-plexes, complements of bounded-degeneracy and bounded-treewidth graphs. Interestingly, our algorithms follow relatively simple backtracking procedures, analogous to what is done in practice. Our results underscore the significance of the c-closed graph class for theoretical understanding of social network analysis.Balaram Behera, Edin Husić, Shweta Jain, Tim Roughgarden, C. Seshadhri, Mark Bravermanwork_a2rfbxa52jcoln4i3j2f7o42omTue, 25 Jan 2022 00:00:00 GMT