We start an investigation into the complexity of variations of the Equal Sum Subsets problem, a basic problem in which we are given a set of numbers and are asked to nd two disjoint subsets of the numbers that add up to the same sum. While Equal Sum Subsets is known to be NP-complete, only very few studies have investigated the complexity of its variations. In this paper, we show NP-completenes...

We study locally spatially homogeneous solutions of the EinsteinVlasov system with a positive cosmological constant. First the global existence of solutions of this system and the casual geodesic completeness are shown. Then the asymptotic behaviour of solutions in the future time is investigated in various aspects.

Given a graph G with a total order defined on its vertices, the Maximum Pagenumber-k Subgraph Problem asks for a maximum subgraph G′ of G such that G′ can be embedded into a k-book when the vertices are placed on the spine according to the specified total order. We show that this problem is NP-complete for k ≥ 2.

We prove strong completeness of a range of substructural logics with respect to their relational semantics by completeness-via-canonicity. Specifically, we use the topological theory of canonical (in) equations in distributive lattice expansions to show that distributive substructural logics are strongly complete with respect to their relational semantics. By formalizing the problem in the lang...

We study א0-stable theories, and prove that if T either has eniDOP or is eni-deep, then its class of countable models is Borel complete. We introduce the notion of λ-Borel completeness and prove that such theories are λ-Borel complete. Using this, we conclude that an א0-stable theory satisfies I∞,א0(T, λ) = 2 λ for all cardinals λ if and only if T either has eni-DOP or is eni-deep.

In this paper we study the interplay between metric and order completeness of semantic domains equipped with generalised distances. We prove that for bounded complete posets directed-completeness and partial metric completeness are interdefinable. Moreover, we demonstrate that Lawson-compact, countably based domains are precisely the compact pmetric spaces that are continuously ordered.

In this paper, we consider the following graph embedding problem: Given a bipartite graph G = (V1, V2;E), where the maximum degree of vertices in V2 is 4, can G be embedded on a two dimensional grid such that each vertex in V1 is drawn as a line segment along a grid line, each vertex in V2 is drawn as a point at a grid point, and each edge e = (u, v) for some u ∈ V1 and v ∈ V2 is drawn as a lin...

We revisit the problem of designing the profit-maximizing single-item auction, solved by Myerson in his seminal paper for the case in which bidder valuations are independently distributed. We focus on general joint distributions, seeking the optimal deterministic incentive compatible auction. We give a geometric characterization of the optimal auction, resulting in a duality theorem and an effi...

Various extensions of the leximin order to the infinite dimensional setting have been suggested. They relax completeness and strong anonymity. Instead, by removing sensitivity to generations at infinite rank this paper defines a complete and strongly anonymous leximin relation on infinite streams. The order is axiomatized, and it is shown to be the limit of extended rank-discounted utilitariani...

In the edge searching problem, searchers move from vertex to vertex in a graph to capture an invisible, fast intruder that may occupy either vertices or edges. Fast searching is a monotonic internal model in which, at every move, a new edge of the graph G must be guaranteed to be free of the intruder. That is, once all searchers are placed the graph G is cleared in exactly |E(G)| moves. Such a ...