Andrei Gagarin

Cardiff University | CU · School of Mathematics

The Kuratowski graphs $K_{3,3}$ and $K_5$ characterize planarity. Counting distinct 2-cell embeddings of these two graphs on orientable surfaces was previously done by using Burnside's Lemma and their automorphism groups, without actually constructing the embeddings. We obtain all 2-cell embeddings of these graphs on the double torus, using a const...

We consider the minimum weight and smallest weight minimum-size dominating set problems in vertex-weighted graphs and networks. The latter problem is a two-objective optimization problem, which is different from the classic minimum weight dominating set problem that requires finding a dominating set of the smallest weight in a graph without trying...

We present new greedy and beam search heuristic methods to find small-size $k$-dominating sets in graphs. The methods are inspired by a new problem formulation which explicitly highlights a certain structure of the problem. An empirical evaluation of the new methods is done with respect to two existing methods, using instances of graphs correspondi...

We present new greedy and beam search heuristic methods to find small-size k-dominating sets in graphs. The methods are inspired by a new problefv m formulation which explicitly highlights a certain structure of the problem. An empirical evaluation of the new methods is done with respect to two existing methods, using instances of graphs correspond...

A novel location obfuscation method for online route planning is proposed which is robust to privacy inferences by the service provider regarding route source and destination. This is achieved by performing the task of route computation in a distributed manner. Specifically, the client decomposes the required route into a sequence of shorter routes...

Terms are linguistic signifiers of domain–specific concepts. Semantic similarity between terms refers to the corresponding distance in the conceptual space. In this study, we use lexico–syntactic information to define a vector space representation in which cosine similarity closely approximates semantic similarity between the corresponding terms. G...

Electric and hybrid vehicles play an increasing role in the road transport networks. Despite their advantages, they have a relatively limited cruising range in comparison to traditional diesel/petrol vehicles, and require significant battery charging time. We propose to model the facility location problem of the placement of charging stations in ro...

A workflow specification defines a set of steps, a set of users, and an access control policy. The policy determines which steps a user is authorized to perform and imposes constraints on which sets of users can perform which sets of steps. The workflow satisfiability problem (WSP) is the problem of determining whether there exists an assignment of...

The fixed parameter tractable (FPT) approach is a powerful tool in tackling computationally hard problems. In this paper we link FPT results to classic artificial intelligence techniques to show how they complement each other. Specifically, we consider the workflow satisfiability problem (WSP) which asks whether there exists an assignment of author...

The workflow satisfiability problem (WSP) asks whether there exists an assignment of authorised users to the steps in a workflow specification, subject to certain constraints on the assignment. (Such an assignment is called valid.) The problem is NP-hard even when restricted to the large class of user-independent constraints. Since the number of st...

Let $G$ be a group. The permutability graph of subgroups of $G$, denoted by $\Gamma(G)$, is a graph having all the proper subgroups of $G$ as its vertices, and two subgroups are adjacent in $\Gamma(G)$ if and only if they permute. In this paper, we classify the finite groups whose permutability graphs are toroidal or projective-planar. In addition,...

A workflow specification defines sets of steps and users. An authorization policy imposes constraints on which users may perform particular steps. Other security requirements, such as separation-of-duty, impose constraints on which groups of users may perform sets of steps. The \emph{workflow satisfiability problem} (WSP) is the problem of determin...

The workflow satisfiability problem (WSP) asks whether there exists an assignment of authorized users to the steps in a workflow specification that satisfies the constraints in the specification. The problem is NP-hard in general, but several subclasses of the problem are known to be fixed-parameter tractable (FPT) when parameterized by the number...

The workflow satisfiability problem (WSP) asks whether there exists an assignment of authorised users to the steps in a workflow specification, subject to certain constraints on the assignment. The problem is NP-hard, and we consider its parameterisation by the number $k$ of steps (as $k$ is usually relatively small in practice). We propose a new f...

We consider (closed neighbourhood) packings and their generalization in graphs called limited packings. A vertex set X in a graph G is a k-limited packing if for any vertex $v\in V(G)$, $\left|N[v] \cap X\right| \le k$, where $N[v]$ is the closed neighbourhood of $v$. The k-limited packing number $L_k(G)$ is the largest size of a k-limited packing...

The workflow satisfiability problem (WSP) is a planning problem. Certain sub-classes of this problem have been shown to be fixed-parameter tractable. In this paper we develop an implementation of an algorithm for WSP that has been shown, in our previous paper, to be fixed-parameter for user-independent constraints. In a set of computational experim...

We consider (closed neighbourhood) packings and their generalization in graphs. A vertex set X in a graph G is a k-limited packing if for any vertex $v\in V(G)$, $\left|N[v] \cap X\right| \le k$, where N[v] is the closed neighbourhood of v. The k-limited packing number $L_k(G)$ of a graph G is the largest size of a k-limited packing in G. Limited p...

The bondage number of a graph is the smallest number of its edges whose removal results in a graph having a larger domination number. We provide constant upper bounds for the bondage number of graphs on topological surfaces, and improve upper bounds for the bondage number in terms of the maximum vertex degree and the orientable and non-orientable g...

We consider four different types of multiple domination and provide new improved upper bounds for the k- and k-tuple domination numbers. They generalize two classical bounds for the domination number and are better than a number of known upper bounds for these two multiple domination parameters. Also, we explicitly present and systematize randomize...

We simplify and further develop the methods and ideas of our earlier work [Ars Comb. 64, 33–49 (2002; Zbl 1073.05525)] to efficiently test embeddability of graphs on the torus. Given a non-planar graph G containing a K 5 -subdivision subgraph, we show that it is possible either to transform the K 5 -subdivision into a certain type of K 3,3 -subdivi...

The bondage number b(G) of a graph G is the smallest number of edges of G whose removal results in a graph having the domination number larger than that of G. We show that, for a graph G having the maximum vertex degree Delta(G) and embeddable on an orientable surface of genus h and a non-orientable surface of genus k, b(G) <= min {Delta(G) + h + 2...

We provide a new heuristic method approach to search for degree-balanced and small weight routing spanning trees in a network. The method is a modification of Kruskal’s minimum spanning tree search algorithm and is based on a distributed search by hierarchical clusters. It provides spanning trees with a lower maximum weighted degree, a bigger diame...

We provide a new upper bound for the α-domination number in terms of a parameter α, 0<α ≤ 1, and graph vertex degrees. This result generalises the well-known Caro-Roditty bound for the domination number of a graph. The same probabilistic construction is used to generalise another well-known upper bound for the classical domination in graphs. Using...

Forbidden minors and subdivisions for toroidal graphs are numerous. We consider the toroidal graphs with no K3,3-subdivisions that coincide with the toroidal graphs with no K3,3-minors. These graphs admit a unique decomposition into planar components and have short lists of obstructions. We provide the complete lists of four forbidden minors and el...

Sensor networks are commonly used for security and surveillance applications. As sensor nodes have limited battery paower, computing, and storage resources, the energy efficient security techniques are needed. We provide a new heuris- tic approach to search for balanced and small weight routing spanning trees in a network. The approach is a modific...

In this paper, we provide an upper bound for the k-tuple domination number that generalises known upper bounds for the double and triple domination numbers. We prove that for any graph G, (gamma xk)(G) <= 1n(delta - k + 2) + 1n (Sigma(k-1)(m=1) (k - m)(d) over cap (m) + epsilon) + 1/delta - k + 2 n, where (gamma xk)(G) is the k-tuple domination num...

We adapt the classical 3-decomposition of any 2-connected graph to the case of simple graphs (no loops or multiple edges). By analogy with the block-cutpoint tree of a connected graph, we deduce from this decomposition a bicolored tree tc(g) associated with any 2-connected graph g, whose white vertices are the 3-components of g (3-connected compone...

We improve the generalized upper bound for the k-tuple domination number given in [A. Gagarin and V. E. Zverovich, Discrete Math. 308, No. 5–6, 880–885 (2008; Zbl 1133.05069)]. Precisely, we show that for any graph G, when k=3, or k=4 and d≤3·2, γ ×k (G)≤ln(δ-k+2)+ln(k-2)d+∑ m=2 k-2 (k-m) 4 min{m,k-2-m} d ^ m +d ^ k-1 +1 δ-k+2n, and, when k=4 and d...

We adapt the classical 3-decomposition of any 2-connected graph to the case of simple graphs (no loops or multiple edges). By analogy with the block-cutpoint tree of a connected graph, we deduce from this decomposition a bicolored tree tc(g) associated with any 2-connected graph g, whose white vertices are the 3-components of g (3-connected compone...

We consider the class T of 2-connected non-planar K3,3-subdivision-free graphs that are embeddable in the torus. We show that any graph in T admits a unique decomposition as a basic toroidal graph (the toroidal core) where the edges are replaced by two-pole networks constructed from 2-connected planar graphs. The structure theorem provides a practi...

Motivation: High-throughput screening (HTS) is an early-stage process in drug discovery which allows thousands of chemical compounds to be tested in a single study. We report a method for correcting HTS data prior to the hit selection process (i.e. selection of active compounds). The proposed correction minimizes the impact of systematic errors wh...

We provide a description of unlabelled enumeration techniques, with complete proofs, for graphs that can be canonically obtained by substituting 2-pole networks for the edges of core graphs. Using structure theorems for toroidal and projective-planar graphs containing no K3,3-subdivisions, we apply these techniques to obtain their unlabelled enumer...

A typical modern high-throughput screening (HTS) operation consists of testing thousands of chemical compounds to select active ones for future detailed examination. The authors describe 3 clustering techniques that can be used to improve the selection of active compounds (i.e., hits). They are designed to identify quality hits in the observed HTS...

We characterize the toroidal graphs with no K3,3-subdivisions as canonical compositions in which 2-pole planar networks are substituted for the edges of non-planar cores. This structure enables us to enumerate these graphs. We describe an explicit enumerative approach that requires unlabelled enumeration of 2-connected planar graphs.

Motivation: High-throughput screening (HTS) plays a central role in modern drug discovery, allowing for testing of >100,000 compounds per screen. The aim of our work was to develop and implement methods for minimizing the impact of systematic error in the analysis of HTS data. To the best of our knowledge, two new data correction methods included...

High-throughput screening (HTS) is an efficient technological tool for drug discovery in the modern pharmaceutical industry. It consists of testing thousands of chemical compounds per day to select active ones. This process has many drawbacks that may result in missing a potential drug candidate or in selecting inactive compounds. We describe and c...

We provide a description of unlabelled enumeration techniques, with complete proofs, for graphs that can be canonically obtained by substituting 2-pole networks for the edges of core graphs. Using structure theorems for toroidal and projective-planar graphs containing no K33-subdivisions, we apply these techniques to obtain their unlabelled enumera...

Forbidden minors and subdivisions for toroidal graphs are numerous. In contrast, the toroidal graphs with no K3,3's have a nice explicit structure and short lists of obstructions. For these graphs, we provide the complete lists of four forbidden minors and eleven forbidden subdivisions.

We describe the structure of 2-connected non-planar toroidal graphs with no K_{3,3}-subdivisions, using an appropriate substitution of planar networks into the edges of certain graphs called toroidal cores. The structural result is based on a refinement of the algorithmic results for graphs containing a fixed K_5-subdivision in [A. Gagarin and W. K...

We consider the class F of 2-connected non-planar K_{3,3}-subdivision-free graphs that are embeddable in the projective plane. We show that these graphs admit a unique decomposition as a graph K_5 (the core) where the edges are replaced by two-pole networks constructed from 2-connected planar graphs. A method to enumerate these graphs in the labell...

Embeddings of graphs on the torus are studied. All 2-cell embeddings of the vertex-transitive graphs on 12 vertices or less are constructed. Their automorphism groups and dual maps are also constructed. A table of embeddings is presented.

Given a non-planar graph G with a subdivision of K5 as a subgraph, we can either transform the K5-subdivision into a K3,3-subdivision if it is possible, or else we obtain a partition of the vertices of G\K5 into equiva- lence classes. As a result, we can reduce a projective planarity or toroidality algorithm to a small constant number of simple pla...

Embeddings of graphs on the torus are studied. All 2-cell embeddings of the vertex-transitive graphs on 12 vertices or less are constructed. Their automorphism groups and dual maps are also constructed. A table of embeddings is presented.

We investigate the connections between families of graphs closed under (induced) subgraphs and their forbidden (induced) subgraph characterizations. In particular, we discuss going from a forbidden subgraph characterization of a family ℙ to a forbidden induced subgraph characterization of the family of line graphs of members of ℙ in the most genera...

desthéo emes de structure classifiant les graphes 2-connexes sans subdivision de K3,3 qui peuven etre plongés sur le plan projectif ou sur le tore. Ces résultats sont formulés en termes d'une opération naturelle de substitution de réseaux bipolaires planaires dans les arêtes de certains graphes appelés noyaux projectifs-planaires ou torodaux. On en...