Solving Mahjong Solitaire boards with peeking

We first prove that solving Mahjong Solitaire boards with peeking is NP-complete, even if one only allows isolated stacks of the forms /aab/ and /abb/. We subsequently show that layouts of isolated stacks of heights one and two can always be solved with peeking, and that doing so is in P, as well as finding an optimal algorithm for such layouts without peeking. Next, we describe a practical algorithm for solving Mahjong Solitaire boards with peeking, which is simple and fast. The algorithm uses an effective pruning criterion and a heuristic to find and prioritize critical groups. The ideas of the algorithm can also be applied to solving Shisen-Sho with peeking.Comment: 10 page

Fred Zacharias’s Skeptical Moralism

Fred Zacharias\u27s articles, Rethinking Confidentiality, published in two parts, were a sensational start to an illustrious career. Fred conducted the first and one of the best empirical studies of confidentiality in years, surveying lawyers and clients in Tompkins County, New York, about what lawyers actually told clients about confidentiality and its exceptions, and what difference the exceptions made in whether clients withheld information from their lawyers

Fiduciary Legal Ethics, Zeal, and Moral Activism

The recent turn to fiduciary theory among private lawyer scholars suggests that lawyer as fiduciary may provide a fresh justification for legal ethics distinct from moral and political accounts propounded by theorists in recent decades. This Article examines the justification and limits of fiduciary legal ethics. In the course of the investigation, it argues that the fiduciary relation of lawyer to client as defined in the ethics codes does not align perfectly with fiduciary principles in other legal domains, such as agency, trust, or corporate law. Lawyers are fiduciaries of their clients. Does that mean lawyers can never throttle back on partisan zeal for moral reasons? So it might seem, and so some scholars have argued. Ethics rules permit lawyers to withdraw from representations they find morally repugnant, but not to represent clients with diminished zeal. And yet there are cases, such as peeking at metadata inadvertently transmitted in documents sent by an adversary, or exploiting scrivener\u27s errors, where many lawyers understandably back off from the sternest implications of partisan zeal. Such cases call into question whether lawyer as fiduciary tells the whole story. An adequate theory of the lawyer-client fiduciary relationship must define the limits to fiduciary zeal as well as justify the fiduciary relationship itself. Otherwise, invoking the word fiduciary merely relabels the moral problem of partisan zeal rather than resolving it

Unit Mixed Interval Graphs

In this paper we extend the work of Rautenbach and Szwarcfiter by giving a structural characterization of graphs that can be represented by the intersection of unit intervals that may or may not contain their endpoints. A characterization was proved independently by Joos, however our approach provides an algorithm that produces such a representation, as well as a forbidden graph characterization

Is the world made of loops?

I see no good reason to prefer (any version I know of) the `holonomy interpretation' to the `potential interpretation' of the Aharonov-Bohm effect. Everyone agrees that the inverse image $[A]=[A+d\lambda]_{\lambda}=d^{-1}F$ of the electromagnetic field $F$ is a class, full of individuals; and that the circulation $\small{\textsf{C}}$ of the electromagnetic potential $A$ around a loop $\sigma_0$ encircling the solenoid is common to the whole class $[A]$, and to the homotopy class or \emph{hoop} $[\sigma_0]$. If picking individuals out of classes is the problem, picking an individual potential out of $[A]$ should be no worse than picking an individual loop out of $[\sigma_0]$. The individuals of $[A]$ can moreover be transcended---punctually, without integration around loops---by an appropriate version of the electromagnetic connection.Comment: comments welcom