Related papers: The Complexity of Surjective Homomorphism Problems…
We present the notion of injective hom-complexity, leading to a connection between the covering number of a group and the sectional number of a group homomorphism, and provide estimates for computing this invariant.
Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms is an important tool.
We first study the higher version of the relative topological complexity by using the homotopic distance. We also introduced the generalized version of the relative topological complexity of a topological pair on both the Schwarz genus and…
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…
Homotopy coherence has a considerable history, albeit also by other names. We provide a brief semi-historical survey providing some links that may not be common knowledge.
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
Trigraph list homomorphism problems (also known as list matrix partition problems) have generated recent interest, partly because there are concrete problems that are not known to be polynomial time solvable or NP-complete. Thus while…
A general problem in complex cobordism theory is to find useful representatives for cobordism classes. One particularly convenient class of complex manifolds consists of smooth projective toric varieties. The bijective correspondence…
A list of open problems on holomorphic symplectic, contact and Poisson manifolds.
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
We define a simpler notion of symmetric topological complexity more ad hoc to the motion planning problem which was the original motivation for the definition of topological complexity. This is a homotopy invariant that we call…
For complexity of the heterogeneous minimum spanning forest problem has not been determined, we reduce 3-SAT which is NP-complete to 2-heterogeneous minimum spanning forest problem to prove this problem is NP-hard and spread result to…
We provide an overview of some recent progress on the complexity of election systems. The issues studied include the complexity of the winner, manipulation, bribery, and control problems.
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…
We survey results on the hardness of approximating combinatorial optimization problems.
We show that the problem to decide whether two (convex) polytopes, given by their vertex-facet incidences, are combinatorially isomorphic is graph isomorphism complete, even for simple or simplicial polytopes. On the other hand, we give a…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
We formalize the concept of a centralizer-respecting homomorphism, surjective homomorphisms which are equivariant with respect to taking the centralizer of a subgroup. There is a functor from the category of centralizer-respecting…