1,594 research outputs found
On Solving Travelling Salesman Problem with Vertex Requisitions
We consider the Travelling Salesman Problem with Vertex Requisitions, where
for each position of the tour at most two possible vertices are given. It is
known that the problem is strongly NP-hard. The proposed algorithm for this
problem has less time complexity compared to the previously known one. In
particular, almost all feasible instances of the problem are solvable in O(n)
time using the new algorithm, where n is the number of vertices. The developed
approach also helps in fast enumeration of a neighborhood in the local search
and yields an integer programming model with O(n) binary variables for the
problem.Comment: To appear in Yugoslav Journal of Operations Researc
On the Complexity of the Constrained Input Selection Problem for Structural Linear Systems
This paper studies the problem of, given the structure of a linear-time
invariant system and a set of possible inputs, finding the smallest subset of
input vectors that ensures system's structural controllability. We refer to
this problem as the minimum constrained input selection (minCIS) problem, since
the selection has to be performed on an initial given set of possible inputs.
We prove that the minCIS problem is NP-hard, which addresses a recent open
question of whether there exist polynomial algorithms (in the size of the
system plant matrices) that solve the minCIS problem. To this end, we show that
the associated decision problem, to be referred to as the CIS, of determining
whether a subset (of a given collection of inputs) with a prescribed
cardinality exists that ensures structural controllability, is NP-complete.
Further, we explore in detail practically important subclasses of the minCIS
obtained by introducing more specific assumptions either on the system dynamics
or the input set instances for which systematic solution methods are provided
by constructing explicit reductions to well known computational problems. The
analytical findings are illustrated through examples in multi-agent
leader-follower type control problems
Computing Unique Maximum Matchings in O(m) time for Konig-Egervary Graphs and Unicyclic Graphs
Let alpha(G) denote the maximum size of an independent set of vertices and
mu(G) be the cardinality of a maximum matching in a graph G. A matching
saturating all the vertices is perfect. If alpha(G) + mu(G) equals the number
of vertices of G, then it is called a Konig-Egervary graph. A graph is
unicyclic if it has a unique cycle.
In 2010, Bartha conjectured that a unique perfect matching, if it exists, can
be found in O(m) time, where m is the number of edges.
In this paper we validate this conjecture for Konig-Egervary graphs and
unicylic graphs. We propose a variation of Karp-Sipser leaf-removal algorithm
(Karp and Spiser, 1981), which ends with an empty graph if and only if the
original graph is a Konig-Egervary graph with a unique perfect matching
obtained as an output as well.
We also show that a unicyclic non-bipartite graph G may have at most one
perfect matching, and this is the case where G is a Konig-Egervary graph.Comment: 10 pages, 5 figure
Partitioning Perfect Graphs into Stars
The partition of graphs into "nice" subgraphs is a central algorithmic
problem with strong ties to matching theory. We study the partitioning of
undirected graphs into same-size stars, a problem known to be NP-complete even
for the case of stars on three vertices. We perform a thorough computational
complexity study of the problem on subclasses of perfect graphs and identify
several polynomial-time solvable cases, for example, on interval graphs and
bipartite permutation graphs, and also NP-complete cases, for example, on grid
graphs and chordal graphs.Comment: Manuscript accepted to Journal of Graph Theor
Optimal Recombination in Genetic Algorithms
This paper surveys results on complexity of the optimal recombination problem
(ORP), which consists in finding the best possible offspring as a result of a
recombination operator in a genetic algorithm, given two parent solutions. We
consider efficient reductions of the ORPs, allowing to establish polynomial
solvability or NP-hardness of the ORPs, as well as direct proofs of hardness
results
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