4,718 research outputs found
On combinatorial optimisation in analysis of protein-protein interaction and protein folding networks
Abstract: Protein-protein interaction networks and protein folding networks represent prominent research topics at the intersection of bioinformatics and network science. In this paper, we present a study of these networks from combinatorial optimisation point of view. Using a combination of classical heuristics and stochastic optimisation techniques, we were able to identify several interesting combinatorial properties of biological networks of the COSIN project. We obtained optimal or near-optimal solutions to maximum clique and chromatic number problems for these networks. We also explore patterns of both non-overlapping and overlapping cliques in these networks. Optimal or near-optimal solutions to partitioning of these networks into non-overlapping cliques and to maximum independent set problem were discovered. Maximal cliques are explored by enumerative techniques. Domination in these networks is briefly studied, too. Applications and extensions of our findings are discussed
More Applications of the d-Neighbor Equivalence: Connectivity and Acyclicity Constraints
In this paper, we design a framework to obtain efficient algorithms for several problems with a global constraint (acyclicity or connectivity) such as Connected Dominating Set, Node Weighted Steiner Tree, Maximum Induced Tree, Longest Induced Path, and Feedback Vertex Set. For all these problems, we obtain 2^O(k)* n^O(1), 2^O(k log(k))* n^O(1), 2^O(k^2) * n^O(1) and n^O(k) time algorithms parameterized respectively by clique-width, Q-rank-width, rank-width and maximum induced matching width. Our approach simplifies and unifies the known algorithms for each of the parameters and match asymptotically also the running time of the best algorithms for basic NP-hard problems such as Vertex Cover and Dominating Set. Our framework is based on the d-neighbor equivalence defined in [Bui-Xuan, Telle and Vatshelle, TCS 2013]. The results we obtain highlight the importance and the generalizing power of this equivalence relation on width measures. We also prove that this equivalence relation could be useful for Max Cut: a W[1]-hard problem parameterized by clique-width. For this latter problem, we obtain n^O(k), n^O(k) and n^(2^O(k)) time algorithm parameterized by clique-width, Q-rank-width and rank-width
More applications of the d-neighbor equivalence: acyclicity and connectivity constraints
In this paper, we design a framework to obtain efficient algorithms for
several problems with a global constraint (acyclicity or connectivity) such as
Connected Dominating Set, Node Weighted Steiner Tree, Maximum Induced Tree,
Longest Induced Path, and Feedback Vertex Set. We design a meta-algorithm that
solves all these problems and whose running time is upper bounded by
, , and where is respectively the clique-width,
-rank-width, rank-width and maximum induced matching width of a
given decomposition. Our meta-algorithm simplifies and unifies the known
algorithms for each of the parameters and its running time matches
asymptotically also the running times of the best known algorithms for basic
NP-hard problems such as Vertex Cover and Dominating Set. Our framework is
based on the -neighbor equivalence defined in [Bui-Xuan, Telle and
Vatshelle, TCS 2013]. The results we obtain highlight the importance of this
equivalence relation on the algorithmic applications of width measures.
We also prove that our framework could be useful for -hard problems
parameterized by clique-width such as Max Cut and Maximum Minimal Cut. For
these latter problems, we obtain , and time
algorithms where is respectively the clique-width, the
-rank-width and the rank-width of the input graph
Total Domination, Separated Clusters, CD-Coloring: Algorithms and Hardness
Domination and coloring are two classic problems in graph theory. The major
focus of this paper is the CD-COLORING problem which combines the flavours of
domination and colouring. Let be an undirected graph. A proper vertex
coloring of is a if each color class has a dominating vertex
in . The minimum integer for which there exists a of
using colors is called the cd-chromatic number, . A set
is a total dominating set if any vertex in has a neighbor
in . The total domination number, of is the minimum
integer such that has a total dominating set of size . A set
is a if no two vertices in lie at a
distance 2 in . The separated-cluster number, , of is the
maximum integer such that has a separated-cluster of size .
In this paper, first we explore the connection between CD-COLORING and TOTAL
DOMINATION. We prove that CD-COLORING and TOTAL DOMINATION are NP-Complete on
triangle-free -regular graphs for each fixed integer . We also
study the relationship between the parameters and .
Analogous to the well-known notion of `perfectness', here we introduce the
notion of `cd-perfectness'. We prove a sufficient condition for a graph to
be cd-perfect (i.e. , for any induced subgraph
of ) which is also necessary for certain graph classes (like triangle-free
graphs). Here, we propose a generalized framework via which we obtain several
exciting consequences in the algorithmic complexities of special graph classes.
In addition, we settle an open problem by showing that the SEPARATED-CLUSTER is
polynomially solvable for interval graphs
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