In previous work of the second author a rigorous mathematical foundation for re-encoding one evolutionary search algorithm by another has been developed. A natural issue to consider then is the complexity of deciding whether or not a given evolutionary algorithm can be re-encoded by one of the standard classical evolutionary algorithms such as a binary genetic algorithm. In the current paper we...

Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, and in particular in the complex systems literature, although its properties are not well understood. We here present first results on the computational and analytical properties of modularity. The complexity status of modularity maximization is r...

Suppose {R1, . . . , Rk} is the set of all possible regions [?] of graph G. Consider a k-dimensional vector C whose i-th entry, C[i], indicates the number of connected components in which G decomposes when all nodes in Ri fails. Then, region-based component decomposition number (RBCDN) of graphG with region R is defined as αR(G) = max1≤i≤k C[i]. Suppose the RBCDN of G with region R is αR(G). If...

A picturesque way to see a large network of links shared by many infinitesimally small selfish users is as a large pipeline infrastructure with users as liquid molecules flowing into it. When the owner of such a selfishly congested network tries to improve its flow speed, the common sense suggests to focus and fix links that seem older and slower. Contrary to this belief, Braess's paradox illus...

In the hedonic coalition formation game model Roles and Teams Hedonic Games (RTHG) (Spradling et al. 2013), agents view teams as compositions of available roles. An agent’s utility for a partition is based upon which role she fulfills within the coalition and which additional roles are being fulfilled within the coalition. Goals for matchmaking in this setting include forming partitions which o...

It is know that determining the satisfiability of n-valued Łukasiewicz rules is NP-complete for n ≥ 4, as well as that it can be solved in time linear in the length of the formula in the Boolean case (when n = 2). However, the complexity for n = 3 is an open problem. In this paper we formally prove that the satisfiability problem for 3-valued Łukasiewicz rules is NP-complete. Moreover, we also ...

In this note, we study under which conditions various sets (even easy ones) can be associated with a witnessing relation that is #P complete. We show a sufficient condition for an NP set to have such a relation. This condition applies also to many NP-complete sets, as well as to many sets in P .

Given two triangulations of a convex polygon, computing the minimum number of flips required to transform one to the other is a long-standing open problem. It is not known whether the problem is in P or NP-complete. We prove that two natural generalizations of the problem are NP-complete, namely computing the minimum number of flips between two triangulations of (1) a polygon with holes; (2) a ...

In the Rectangle Escape problem, we are given a set of rectangles S in a rectangular region R, and we would like to extend these rectangles to one of the four sides of R while ensuring that the maximum number of overlaps is minimized. More formally, define the density of a point p in R as the number of extended rectangles that contain p. The question is then to find an extension with the smalle...

The problem Cover(H) asks whether an input graph G covers a fixed graph H (i.e., whether there exists a homomorphism G → H which locally preserves the structure of the graphs). Complexity of this problem has been intensively studied. In this paper, we consider the problem PlanarCover(H) which restricts the input graph G to be planar. PlanarCover(H) is polynomially solvable if Cover(H) belongs t...