Related papers: On the Path-Width of Integer Linear Programming
Graph polynomials which are definable in Monadic Second Order Logic (MSOL) on the vocabulary of graphs are Fixed-Parameter Tractable (FPT) with respect to clique-width. In contrast, graph polynomials which are definable in MSOL on the…
Due to their importance in practice, dominating set problems in graphs have been greatly studied in past and different formulations of these problems are presented in literature. This paper's focus is on two problems: weakly convex…
Lineage tracing, the tracking of living cells as they move and divide, is a central problem in biological image analysis. Solutions, called lineage forests, are key to understanding how the structure of multicellular organisms emerges. We…
Stable Logic Programming (SLP) is an emergent, alternative style of logic programming: each solution to a problem is represented by a stable model of a deductive database/function-free logic program encoding the problem itself. Several…
We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is as…
It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…
The problem of finding a path between two points while avoiding obstacles is critical in robotic path planning. We focus on the feasibility problem: determining whether such a path exists. We model the robot as a query-specific rectangular…
Integer programming (IP) has proven to be highly effective in solving many path-based optimization problems in robotics. However, the applications of IP are generally done in an ad-hoc, problem specific manner. In this work, after examined…
This paper introduces a novel decision-making framework that promotes consistency among decisions made by diverse models while utilizing external knowledge. Leveraging the Integer Linear Programming (ILP) framework, we map predictions from…
Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…
In this paper, we introduce a new class of parameterized problems, which we call XALP: the class of all parameterized problems that can be solved in $f(k)n^{O(1)}$ time and $f(k)\log n$ space on a non-deterministic Turing Machine with…
Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called "iterated…
The class XNLP consists of (parameterized) problems that can be solved nondeterministically in $f(k)n^{O(1)}$ time and $f(k)\log n$ space, where $n$ is the size of the input instance and $k$ the parameter. The class XALP consists of…
In the Integer Quadratic Programming problem input is an n*n integer matrix Q, an m*n integer matrix A and an m-dimensional integer vector b. The task is to find a vector x in Z^n, minimizing x^TQx, subject to Ax <= b. We give a fixed…
We introduce and study the Separation Problem for infinite graphs, which involves determining whether a connected graph splits into at least two infinite connected components after the removal of a given finite set of edges. We prove that…
The proof of information inequalities and identities under linear constraints on the information measures is an important problem in information theory. For this purpose, ITIP and other variant algorithms have been developed and…
We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of…
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
We consider the problem of finding a Hamiltonian path with precedence constraints in the form of a partial order on the vertex set. This problem is known as Partially Ordered Hamiltonian Path Problem (POHPP). Here, we study the complexity…
This letter concerns optimal power transmission line inspection formulated as a proposed generalization of the traveling salesman problem for a multi-route one-depot scenario. The problem is formulated for an inspection vehicle with a…