Voting schemes are common social choice function that allow voters to aggregate their preferences in a socially desirable way. Unfortunately, the GibbardSatterthwaite theorem states that many of these schemes are susceptible to manipulation. Thus, a highly desirable quality, such that a scheme is resistant to manipulaion, is lacking in voting schemes. Since non-manipulability cannot be guarante...

In the offline list update problem, we maintain an unsorted linear list used as a dictionary. Accessing the item at position i in the list costs i units. In order to reduce access cost, we are allowed to update the list at any time by transposing consecutive items at a cost of one unit. Given a sequence of requests one has to serve in turn, we are interested in the minimal cost needed to serve ...

Two subproblems that arise when routing channels with interchangeable terminals are shown to be NP-hard. These problems are: P1: Is there a net to terminal assignment that results in an acyclic vertical constraint graph? P2: For instances with acyclic vertical constraint graphs, obtain net to terminal assignments for which the length of the longest path in the vertical constraint graph is minimum.

Unit disk graphs are the intersection graphs of unit diameter closed disks in the plane. This paper reduces SATISFIABILITY to the problem of recognizing unit disk graphs. Equivalently, it shows that determining if a graph has sphericity 2 or less, even if the graph is planar or is known to have sphericity at most 3, is NP-hard. We show how this reduction can be extended to 3 dimensions, thereby...

Usually, in data processing, to find the parameters of the models that best fits the data, people use the Least Squares method. One of the advantages of this method is that for linear models, it leads to an easy-to-solve system of linear equations. A limitation of this method is that even a single outlier can ruin the corresponding estimates; thus, more robust methods are needed. In particular,...

Art Gallery Localization (AGL) is the problem of placing a set T of broadcast towers in a simple polygon P in order for a point to locate itself in the interior. For any point p ∈ P : for each tower t ∈ T ∩ V (p) (where V (p) denotes the visibility polygon of p) the point p receives the coordinates of t and the Euclidean distance between t and p. From this information p can determine its coordi...

IV-matching is a generalization of perfect bipartite matching. The complexity of finding IV-matching in a graph was posted as an open problem at the ICALP 2014 conference. In this note, we resolve the question and prove that, contrary to the expectations of the authors, the given problem is strongly NP-hard (already in the simplest non-trivial case of four layers). Hence it is unlikely that the...

We answer, in the affirmitive, the following question proposed by Mike Steel as a $100 challenge: “Is the following problem NP hard? Given a ternary phylogenetic X-tree T and a collection Q of quartet subtrees on X, is T the only tree that displays Q?” [25,27]

A generally-accepted minimum requirement for an algorithm to be considered ‘efficient’ is that its running time is polynomial: O(nc) for some constant c, where n is the size of the input.1 Researchers recognized early on that not all problems can be solved this quickly, but we had a hard time figuring out exactly which ones could and which ones couldn’t. there are several so-called NP-hard prob...

1 I n t r o d u c t i o n This paper investigates the problem of realizing a given graph G as a "nearest neighbour graph" of a set P of points in the plane. Roughly speaking, a "nearest neighbour graph" is a geometric graph formed from a set of points in the plane by joining two points if one is the nearest neighbour of the other. Fig. 1. A mutual nearest neighbour graph One specific kind of ne...