419,876 research outputs found
Conflict-Free Coloring of Planar Graphs
A conflict-free k-coloring of a graph assigns one of k different colors to
some of the vertices such that, for every vertex v, there is a color that is
assigned to exactly one vertex among v and v's neighbors. Such colorings have
applications in wireless networking, robotics, and geometry, and are
well-studied in graph theory. Here we study the natural problem of the
conflict-free chromatic number chi_CF(G) (the smallest k for which
conflict-free k-colorings exist). We provide results both for closed
neighborhoods N[v], for which a vertex v is a member of its neighborhood, and
for open neighborhoods N(v), for which vertex v is not a member of its
neighborhood.
For closed neighborhoods, we prove the conflict-free variant of the famous
Hadwiger Conjecture: If an arbitrary graph G does not contain K_{k+1} as a
minor, then chi_CF(G) <= k. For planar graphs, we obtain a tight worst-case
bound: three colors are sometimes necessary and always sufficient. We also give
a complete characterization of the computational complexity of conflict-free
coloring. Deciding whether chi_CF(G)<= 1 is NP-complete for planar graphs G,
but polynomial for outerplanar graphs. Furthermore, deciding whether
chi_CF(G)<= 2 is NP-complete for planar graphs G, but always true for
outerplanar graphs. For the bicriteria problem of minimizing the number of
colored vertices subject to a given bound k on the number of colors, we give a
full algorithmic characterization in terms of complexity and approximation for
outerplanar and planar graphs.
For open neighborhoods, we show that every planar bipartite graph has a
conflict-free coloring with at most four colors; on the other hand, we prove
that for k in {1,2,3}, it is NP-complete to decide whether a planar bipartite
graph has a conflict-free k-coloring. Moreover, we establish that any general}
planar graph has a conflict-free coloring with at most eight colors.Comment: 30 pages, 17 figures; full version (to appear in SIAM Journal on
Discrete Mathematics) of extended abstract that appears in Proceeedings of
the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA
2017), pp. 1951-196
Dealing with Qualitative and Quantitative Features in Legal Domains
In this work, we enrich a formalism for argumentation by including a formal
characterization of features related to the knowledge, in order to capture
proper reasoning in legal domains. We add meta-data information to the
arguments in the form of labels representing quantitative and qualitative data
about them. These labels are propagated through an argumentative graph
according to the relations of support, conflict, and aggregation between
arguments.Comment: arXiv admin note: text overlap with arXiv:1903.0186
Socratic Metaethics Imagined
This is an imagined dialogue between one of the more famous skeptics regarding moral attribution, Thrasymachus, and an imagined Socrates who, through the convenient miracle of time travel, returns to Athens after exposure to contemporary metaethics, now a devoted and formidable quasi-realist expressivist. The dialogue focuses on the characterization of moral conflict and moral justification available to the expressivist, and the authors attempt to lay out the distinctive strengths and weaknesses of the expressivist view
Heterochronic Representations of the Fall : Bakhtin, Milton, DeLillo
Bakhtin argues that each literary genre codifies a particular world-view which is defined, in part, by its chronotope. That is, the spatial and temporal configurations of each genre determine in large part the kinds of action a fictional character may undertake in that given world (without being iconoclastic, a realist hero cannot slay mythical beasts, and a questing knight cannot philosophize over drinks in a cafĂ©). Recent extensions of Bakhtinâs theory have sought to define the chronotopes of new and emergent genres such as the road movie, the graphic novel, and hypertext fiction. Others have challenged Bakhtinâs characterization of certain chronotopes, such as those of epic and lyric poetry, arguing that these genres (and their chronotopes) are far more dynamic and dialogic than Bakhtinâs analysis seems at first glance to allow. Rather than taking issue with Bakhtinâs characterization of particular genres here, however, I wish to argue that we should pay closer attention to the heterochrony, or interplay of different chronotopes, in individual texts and their genres. As Bakhtinâs own essay demonstrates, what makes any literary chronotope dynamic is its conflict and interplay with alternative chronotopes and world-views. Heterochrony (raznovremennost) is the spatiotemporal equivalent of linguistic heteroglossia, and if we examine any of Bakhtinâs readings of particular chronotopes closely enough, we will find evidence of heterochronic conflict. This clash of spatiotemporal configurations within a text, or family of texts, provides the ground for the dialogic inter-illumination of opposing world-views
Strategy-proof allocation mechanisms for economies with public goods
This paper provides a characterization of the class of incentive compatible (i.e., strategy-proof) allocation mechanisms for decision problems associated with classical economic environments. It is shown that when at least one public good is provided, then only dictatorial allocation mechanisms are incentive compatible. Dictatorial mechanisms are very unsatisfactory, as any conflict of interest is always resolved in favor of a single individual (the dictator). This result reveals a basic incompatibility between incentive compatibility and any other desirable property (e.g., any kind of efficiency, fairness, etc.) of an allocation mechanism. In particular, incentive compatible allocation mechanisms typically produce inefficient outcomes
Multidimentional Cheap Talk
In this paper, we extend the cheap talk model of Crawford and Sobel (1982) to a multidimensional state space. We provide a characterization of informative equilibria. Most importantly, we prove for a generic family of distribution functions, that no information transmission is feasible when the conflict between the sender and the receiver is too large. Thus, adding more dimensions cannot improve upon information revelation when interests are too divergentCheap Talk
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