1,653 research outputs found
Local Conflict Coloring
Locally finding a solution to symmetry-breaking tasks such as
vertex-coloring, edge-coloring, maximal matching, maximal independent set,
etc., is a long-standing challenge in distributed network computing. More
recently, it has also become a challenge in the framework of centralized local
computation. We introduce conflict coloring as a general symmetry-breaking task
that includes all the aforementioned tasks as specific instantiations ---
conflict coloring includes all locally checkable labeling tasks from
[Naor\&Stockmeyer, STOC 1993]. Conflict coloring is characterized by two
parameters and , where the former measures the amount of freedom given
to the nodes for selecting their colors, and the latter measures the number of
constraints which colors of adjacent nodes are subject to.We show that, in the
standard LOCAL model for distributed network computing, if l/d \textgreater{}
\Delta, then conflict coloring can be solved in rounds in -node graphs with maximum degree
, where ignores the polylog factors in . The
dependency in~ is optimal, as a consequence of the lower
bound by [Linial, SIAM J. Comp. 1992] for -coloring. An important
special case of our result is a significant improvement over the best known
algorithm for distributed -coloring due to [Barenboim, PODC 2015],
which required rounds. Improvements for other
variants of coloring, including -list-coloring,
-edge-coloring, -coloring, etc., also follow from our general
result on conflict coloring. Likewise, in the framework of centralized local
computation algorithms (LCAs), our general result yields an LCA which requires
a smaller number of probes than the previously best known algorithm for
vertex-coloring, and works for a wide range of coloring problems
The switch operators and push-the-button games: a sequential compound over rulesets
We study operators that combine combinatorial games. This field was initiated
by Sprague-Grundy (1930s), Milnor (1950s) and Berlekamp-Conway-Guy (1970-80s)
via the now classical disjunctive sum operator on (abstract) games. The new
class consists in operators for rulesets, dubbed the switch-operators. The
ordered pair of rulesets (R 1 , R 2) is compatible if, given any position in R
1 , there is a description of how to move in R 2. Given compatible (R 1 , R 2),
we build the push-the-button game R 1 R 2 , where players start by playing
according to the rules R 1 , but at some point during play, one of the players
must switch the rules to R 2 , by pushing the button ". Thus, the game ends
according to the terminal condition of ruleset R 2. We study the pairwise
combinations of the classical rulesets Nim, Wythoff and Euclid. In addition, we
prove that standard periodicity results for Subtraction games transfer to this
setting, and we give partial results for a variation of Domineering, where R 1
is the game where the players put the domino tiles horizontally and R 2 the
game where they play vertically (thus generalizing the octal game 0.07).Comment: Journal of Theoretical Computer Science (TCS), Elsevier, A
Para{\^i}tr
A polynomial version of Cereceda's conjecture
Let k and d be such that k ≥ d + 2. Consider two k-colourings of a d-degenerate graph G. Can we transform one into the other by recolouring one vertex at each step while maintaining a proper coloring at any step? Cereceda et al. answered that question in the affirmative, and exhibited a recolouring sequence of exponential length. However, Cereceda conjectured that there should exist one of quadratic length. The k-reconfiguration graph of G is the graph whose vertices are the proper k-colourings of G, with an edge between two colourings if they differ on exactly one vertex. Cereceda's conjecture can be reformulated as follows: the diameter of the (d + 2)-reconfiguration graph of any d-degenerate graph on n vertices is O(n 2). So far, the existence of a polynomial diameter is open even for d = 2. In this paper, we prove that the diameter of the k-reconfiguration graph of a d-degenerate graph is O(n d+1) for k ≥ d + 2. Moreover, we prove that if k ≥ 3 2 (d + 1) then the diameter of the k-reconfiguration graph is quadratic, improving the previous bound of k ≥ 2d + 1. We also show that the 5-reconfiguration graph of planar bipartite graphs has quadratic diameter, confirming Cereceda's conjecture for this class of graphs
Consumer Brand Relationships Research: A Bibliometric Citation Meta-Analysis
This study examines how scholarly research on consumer brand relationships has evolved over the last decades by conducting a bibliometric citation meta-analysis. The bibliography was compiled using the ISI Web of Science database. The literature review includes 392 papers by 685 authors in 101 journals. The area of consumer brand relationships research is notably interdisciplinary, with articles mainly published in journals for business and management, but also applied psychology and communication. We show the impact of universities, authors, journals, and key articles and outline possible future research avenues. The study explores seven sub-research streams and visualizes how articles on consumer brand relationships build on each other using co-citation mapping technique. Based on the results of this analysis we propose an agenda for future research that offers the potential to advance research on the relationships between consumers and brands
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