The connected dominating set (CDS) problem is a well studied NP-hard problem with many important applications. Dorn et al. [ESA2005, LNCS3669,pp95-106] introduce a new technique to generate 2(O)(root n) time and fixed...
详细信息
ISBN:
(纸本)9783642174605
The connected dominating set (CDS) problem is a well studied NP-hard problem with many important applications. Dorn et al. [ESA2005, LNCS3669,pp95-106] introduce a new technique to generate 2(O)(root n) time and fixed-parameter algorithms for a number of non-local hard problems, including the CDS problem in planar graphs. The practical performance of this algorithm is yet to be evaluated. We perform a computational study for such an evaluation. The results show that the size of instances can be solved by the algorithm mainly depends on the branchwidth of the instances, coinciding with the theoretical result. For graphs with small or moderate branchwidth, the CDS problem instances with size up to a few thousands edges can be solved in a practical time and memory space. This suggests that the branch-decomposition based algorithms can be practical for the planar CDS problem.
The outerplanarity index of a planar graph G is the smallest k such that G has a k-outerplanar embedding. We show how to compute the outerplanarity index of an P.-vertex planar graph in O(n(2)) time, improving the pre...
详细信息
ISBN:
(纸本)9783540755197
The outerplanarity index of a planar graph G is the smallest k such that G has a k-outerplanar embedding. We show how to compute the outerplanarity index of an P.-vertex planar graph in O(n(2)) time, improving the previous best bound of O(k(3)n(2)). Using simple variations of the computation we can determine the radius of a planar graph in O(n(2)) time and its depth in O(n(3)) time. We also give a linear-time 4-approximation algorithm for the outerplanarity index and show how it can be used to solve maximum independent set and several other NP-hard problems faster on planar graphs with outerplanarity index within a constant factor of their treewidth.
We present a method for reducing the treewidth of a graph while preserving all the minimal s - t separators. This technique turns out to be very useful for establishing the fixed-parameter tractability of constrained ...
详细信息
ISBN:
(纸本)9783939897163
We present a method for reducing the treewidth of a graph while preserving all the minimal s - t separators. This technique turns out to be very useful for establishing the fixed-parameter tractability of constrained separation and bipartization problems. To demonstrate the power of this technique, we prove the fixed-parameter tractability of a number of well-known separation and bipartization problems with various additional restrictions (e.g., the vertices being removed from the graph form an independent set). These results answer a number of open questions in the area of parameterized complexity.
Many complex systems that exist in nature and societycan be expressed in terms of networks (e.g., social networks,communication networks, biological networks, Web graph, amongothers). Usually a node represents an enti...
详细信息
Many complex systems that exist in nature and societycan be expressed in terms of networks (e.g., social networks,communication networks, biological networks, Web graph, amongothers). Usually a node represents an entity while an edgerepresents an interaction between two entities. A community arisesin a network when two or more entities have common interests,e.g., related proteins, industrial sectors, groups of people,documents of a collection. There exist applications that model acommunity as a fixed graph H [98, 10, 119, 2, 142, 136].Additionally, it is not expected that an entity of the networkbelongs to only one community; that is, communities tend to sharetheir members. The community discovering or community detectionproblem consists on finding all communities in a given *** problem has been extensively studied from a practicalperspective [61, 137, 122, 116]. However, we believe that thisproblem also brings many interesting theoretical questions. Thus inthis thesis, we will address this problem using a more rigorousapproach. To that end, we first introduce graph problems that weconsider capture well the community discovering problem. Thesegraph problems generalize the classical H-Packing problem [88] intwo different ways. In the H-Packing with t-Overlap problem, thegoal is to find in a given graph G (the network) at least ksubgraphs (the communities) isomorphic to a member of a family ofgraphs H (the community models) such that each pair of subgraphsoverlaps in at most t vertices (the shared members). On the otherhand, in the H-Packing with t-Membership problem instead oflimiting the pairwise overlap, each vertex of G is contained in atmost t subgraphs of the solution. For both problems each member ofH has at most r vertices and m edges. An instance of the H-Packingwith t-Overlap and t-Membership problems corresponds to aninstance of the H-Packing problem for t = 0 and t = 1,respectively. We also restrict the overlap between the edges ofthe subgraphs
Explainable clustering provides human-understandable reasons for decisions in black -box learning models. In a previous work, a decision tree built on the set of dimensions was used to define ranges of values for k-me...
详细信息
Explainable clustering provides human-understandable reasons for decisions in black -box learning models. In a previous work, a decision tree built on the set of dimensions was used to define ranges of values for k-means clusters. For explainable graph clustering, we use expander graphs instead of dense subgraphs since powering an expander graph is guaranteed to result in a clique after at most a logarithmic number of steps. Consider a set of multi-dimensional points labeled with k labels. We introduce the heat map sorting problem as reordering the rows and columns of an input matrix (each point is a column and each row is a dimension) such that the labels of the entries of the matrix form connected components (clusters). A cluster is preserved if it remains connected, i.e., if it is not split into several clusters and no two clusters are merged. In the massively parallel computation model (MPC), each machine has a sublinear memory and the total memory of the machines is linear. We prove the problem is NP-hard. We give a fixed -parameter algorithm in MPC and an approximation algorithm based on expander decomposition. We empirically compare our algorithm with explainable k-means on several graphs of email and computer networks.
The DIRECTED FEEDBACK VERTEX SET (DFVS) problem takes as input a directed graph G and seeks a smallest vertex set S that hits all cycles in G. This is one of Karp's 21 NP-complete problems. Resolving the parameter...
详细信息
The DIRECTED FEEDBACK VERTEX SET (DFVS) problem takes as input a directed graph G and seeks a smallest vertex set S that hits all cycles in G. This is one of Karp's 21 NP-complete problems. Resolving the parameterized complexity status of DFVS was a long-standing open problem until Chen et al. (2008) showed its fixed-parameter tractability via a 4kk!nO(1)-time algorithm, where k = |S|. Here we show fixed-parameter tractability of two generalizations of DFVS:center dot Find a smallest vertex set S such that every strong component of G - S has size at most s: we give an algorithm solving this problem in time 4k(ks + k + s)! middot nO(1). This generalizes an algorithm by Xiao (2017) for the undirected version of the *** dot Find a smallest vertex set S such that every non-trivial strong component of G - S is 1-out-regular: we give an algorithm solving this problem in time 2O(k3) middot nO(1). We also solve the corresponding arc versions of these problems by fixed-parameter algorithms. (c) 2022 Published by Elsevier B.V.
Community detection is an important task in the analysis of biological, social or technical networks. We survey different models of cohesive graphs, commonly referred to as clique relaxations, that are used in the det...
详细信息
Community detection is an important task in the analysis of biological, social or technical networks. We survey different models of cohesive graphs, commonly referred to as clique relaxations, that are used in the detection of network communities. For each clique relaxation, we give an overview of basic model properties and of the complexity of the problem of finding large cohesive subgraphs under this model. Since this problem is usually NP-hard, we focus on combinatorial fixed-parameter algorithms exploiting typical structural properties of input networks.
This paper deals with the problem of enumerating all minimum-cost LCA-reconciliations involving gene duplications and lateral gene transfers (LGTs) for a given species tree S and a given gene tree G. Previously, [Tofi...
详细信息
This paper deals with the problem of enumerating all minimum-cost LCA-reconciliations involving gene duplications and lateral gene transfers (LGTs) for a given species tree S and a given gene tree G. Previously, [Tofigh A, Hallett M, Lagergren J, Simultaneous identification of duplications and lateral gene transfers, IEEE/ACM Trans Comput Biol Bioinf 517-535, 2011.] gave a fixed-parameter algorithm for this problem that runs in O(m + 3(k)n) time, where m is the number of vertices in S, n is the number of vertices in G, and k is the minimum cost of an LCA-reconciliation between S and G. In this paper, by refining their algorithm, we obtain a new one for the same problem that finds and outputs the solutions in a compact form within O(mn(2) + 3(k)) time. In the most interesting case where 3(k) >= mn(2) , our algorithm is O(n) times faster.
Manipulation models for electoral systems are a core research theme in social choice theory; they include bribery (unweighted, weighted, swap, shift,...), control (by adding or deleting voters or candidates), lobbying...
详细信息
Manipulation models for electoral systems are a core research theme in social choice theory; they include bribery (unweighted, weighted, swap, shift,...), control (by adding or deleting voters or candidates), lobbying in referenda and others. We develop a unifying framework for manipulation models with few types of people, one of the most commonly studied scenarios. A critical insight of our framework is to separate the descriptive complexity of the voting rule R from the number of types of people. This allows us to finally settle the computational complexity of R-Swap Bribery, one of the most fundamental manipulation problems. In particular, we prove that R-Swap Bribery is fixed-parameter tractable when R is Dodgson's rule and Young's rule, when parameterized by the number of candidates. This way, we resolve a long-standing open question from 2007 which was explicitly asked by Faliszewski et al. [JAIR 40, 2011]. Our algorithms reveal that the true hardness of bribery problems often stems from the complexity of the voting rules. On one hand, we give a fixed-parameter algorithm parameterized by number of types of people for complex voting rules. Thus, we reveal that R-Swap Bribery with Dodgson's rule is much harder than with Condorcet's rule, which can be expressed by a conjunction of linear inequalities, while Dodson's rule requires quantifier alternation and a bounded number of disjunctions of linear systems. On the other hand, we give an algorithm for quantifier-free voting rules which is parameterized only by the number of conjunctions of the voting rule and runs in time polynomial in the number of types of people. This way, our framework explains why Shift Bribery is polynomial-time solvable for the plurality voting rule, making explicit that the rule is simple in that it can be expressed with a single linear inequality, and that the number of voter types is polynomial.
暂无评论