102,124 research outputs found
Homomorphism Reconfiguration via Homotopy
No full textWe consider the following problem for a fixed graph H: given a graph G and two H-colorings of G, i.e. homomorphisms from G to H, can one be transformed into the other by changing one color at a time, maintaining an H-coloring throughout.This is the same as finding a path in the Hom(G,H) complex. For H=K_k this is the problem of finding paths between k-colorings, which was recently shown to be in P for k\leq 3 and PSPACE-complete otherwise (Bonsma and Cereceda 2009, Cereceda et al. 2011).
We generalize the positive side of this dichotomy by providing an algorithm that solves the problem in polynomial time for any H with no C_4 subgraph. This gives a large class of constraints for which finding solutions to the Constraint Satisfaction Problem is NP-complete, but paths in the solution space can be found in polynomial time.
The algorithm uses a characterization of possible reconfiguration sequences (that is, paths in Hom(G,H)), whose main part is a purely topological condition described in terms of the fundamental groupoid of H seen as a topological space
The Complexity of Promise SAT on Non-Boolean Domains
No full textWhile 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin, Guruswami, and Håstad [FOCS'14/SICOMP'17] proved a result known as "(2+ε)-SAT is NP-hard". They showed that the problem of distinguishing k-CNF formulas that are g-satisfiable (i.e. some assignment satisfies at least g literals in every clause) from those that are not even 1-satisfiable is NP-hard if g/k < 1/2 and is in P otherwise. We study a generalisation of SAT on arbitrary finite domains, with clauses that are disjunctions of unary constraints, and establish analogous behaviour. Thus we give a dichotomy for a natural fragment of promise constraint satisfaction problems (PCSPs) on arbitrary finite domains
Edge Bipartization Faster Than 2^k
No full textIn the EDGE BIPARTIZATION problem one is given an undirected graph G and an integer k, and the question is whether k edges can be deleted from G so that it becomes bipartite. In 2006, Guo et al. [J. Comput. Syst. Sci., 72(8):1386-1396, 2006] proposed an algorithm solving this problem in time O(2^k m^2); today, this algorithm is a textbook example of an application of the iterative compression technique. Despite extensive progress in the understanding of the parameterized complexity of graph separation problems in the recent years, no significant improvement upon this result has been yet reported. We present an algorithm for Edge Bipartization that works in time O(1.977^k nm), which is the first algorithm with the running time dependence on the parameter better than 2^k. To this end, we combine the general iterative compression strategy of Guo et al. [J. Comput. Syst. Sci., 72(8):1386-1396, 2006], the technique proposed by Wahlström [SODA'14] of using a polynomial-time solvable relaxation in the form of a Valued Constraint Satisfaction Problem to guide a bounded-depth branching algorithm, and an involved Measure&Conquer analysis of the recursion tree
Improved hardness for H-colourings of G-colourable graphs
No full textWe present new results on approximate colourings of graphs and, more generally, approximate H-colourings and promise constraint satisfaction problems.
First, we show NP-hardness of colouring k-colourable graphs with colours for every k ≥ 4. This improves the result of Bulín, Krokhin, and Opršal [STOC'19], who gave NP-hardness of colouring k-colourable graphs with 2k – 1 colours for k ≥ 3, and the result of Huang [APPROX-RANDOM'13], who gave NP-hardness of colouring k-colourable graphs with colours for sufficiently large k. Thus, for k ≥ 4, we improve from known linear/sub-exponential gaps to exponential gaps.
Second, we show that the topology of the box complex of H alone determines whether H-colouring of G-colourable graphs is NP-hard for all (non-bipartite, H-colourable) G. This formalises the topological intuition behind the result of Krokhin and Opršal [FOCS’19] that 3-colouring of G-colourable graphs is NP-hard for all (3-colourable, non-bipartite) G. We use this technique to establish NP-hardness of H-colouring of G-colourable graphs for H that include but go beyond K3, including square-free graphs and circular cliques (leaving K4 and larger cliques open).
Underlying all of our proofs is a very general observation that adjoint functors give reductions between promise constraint satisfaction problems.
The full version [55] containing detailed proofs is available at https://arxiv.org/abs/1907.00872.</p
Bibliographie Hilarion G. Petzold 1958 – 2009 mit Anhang als Einführung
No full textDieses Archiv enthält die Gesamtbibliographie der Werke des Autors nebst einiger Texte „Über H. G. Petzold“ im Schlussteil der Bibliographie sowie einen Anhang mit einer Einführung in die Architektur des Werkes in seinem wissenslogischen Aufbau als Ausarbeitung seines „Tree of Science Modells“ (2007).This archive contains the complete bibliography of the author and some texts about H. G. Petzold, moreover an epilogue with an introduction to the architecture of the works in its epistemological structure and composition and as an elaborations of Petzold’s „Tree of Science Modell (2007).https://www.fpi-publikation.de/polyloge/01-2009-petzold-h-g-gesamtbibliographie-h-g-petzold-1958-2009-updating-november2009/peerReviewedpublishedVersio
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Recommended from our members
3346: Samuel G. Freedman, author, 2013
No full textPhotograph of author Samuel G. Freedman, at NT Daily Slash meeting in the Mayborn School of Journalism at UNT
The Right to Strike under the United States Constitution: Theory, Practice, and Possible Implications for Canada
No full textAnswering critics of the Canadian Supreme Court's judgment in B.C. Health, the author argues that the Court laid the foundation for a principled and durable doctrine protecting constitutional labour rights, one that goes directly to the heart of the matter — the inequality of workers’ power in the employment relation. In the author’s view, two paths could lead from B.C. Health to the recognition of Charter protec- tion for a right to strike: one that treats the right as an accessory to col- lective bargaining, and one that upholds the right directly on the basis of the Charter values of equality and participation. The author supports the latter approach, contending that constitutional rights should be defined in relation to fundamental values, in a way that is not contingent on time-bound or fact-sensitive assessments about the role of strikes within a particular collective bargaining regime. Although a Charter right to strike may involve the courts in difficult choices about when to defer to legislative policy decisions, and courts may lack the institutional capac- ity to deal effectively with labour law issues, the author points out that judges can look to ILO standards for expert guidance. Noting that the U.S. experience in this area might be of considerable use to Canadians, the author concludes by providing an overview of American case law concerning a constitutional right to strike.Peer reviewe
G-Rank: Unsupervised Continuous Learn-to-Rank for Edge Devices in a P2P Network
No full textRanking algorithms in traditional search engines are powered by enormous training data sets that are meticulously engineered and curated by a centralized entity. Decentralized peer-to-peer (p2p) networks such as torrenting applications and Web3 protocols deliberately eschew centralized databases and computational architectures when designing services and features. As such, robust search-and-rank algorithms designed for such domains must be engineered specifically for decentralized networks, and must be lightweight enough to operate on consumer-grade personal devices such as a smartphone or laptop computer. We introduce G-Rank, an unsupervised ranking algorithm designed exclusively for decentralized networks. We demonstrate that accurate, relevant ranking results can be achieved in fully decentralized networks without any centralized data aggregation, feature engineering, or model training. Furthermore, we show that such results are obtainable with minimal data preprocessing and computational overhead, and can still return highly relevant results even when a user’s device is disconnected from the network. G-Rank is highly modular in design, is not limited to categorical data, and can be implemented in a variety of domains with minimal modification. The results herein show that unsupervised ranking models designed for decentralized p2p networks are not only viable, but worthy of further research.https://github.com/awrgold/G-RankComputer Scienc
- …
