A sequence d = (d1, d2, . . ., dn) of positive integers is graphic if it is the degree sequence of some simple graph G, and planaric if it is the degree sequence of some simple planar graph G. It is known that if ∑ d...
详细信息
Katz centrality measures a node’s influence within a network, considering the total number of walks between pairs of nodes rather than solely the shortest paths. This paper presents an algorithm for dynamically updat...
详细信息
A variation of the vertex cover problem is the eternal vertex cover problem. This is a two-player (attacker and defender) game, where the defender must allocate guards at specific vertices in order for those vertices ...
详细信息
ISBN:
(纸本)9783031522123;9783031522130
A variation of the vertex cover problem is the eternal vertex cover problem. This is a two-player (attacker and defender) game, where the defender must allocate guards at specific vertices in order for those vertices to form a vertex cover. The attacker can attack one edge at a time. The defender must move the guards along the edges so that at least one guard passes through the attacked edge (guard moves from one end point of the attacked edge to the another end point), and the new configuration still acts as a vertex cover. If the defender is unable to make such a maneuver, the attacker prevails. If a strategy for defending the graph against any infinite series of attacks emerges, the defender wins. The eternal vertex cover problem is to find the smallest number of guards with which the defender can develop a successful strategy. The same problem is referred as the eternal connected vertex cover problem if the following additional requirement is added: underlying vertices of each defensive configuration form a connected vertex cover. The smallest number of guards that can be used to create a successful defensive strategy, in this case, is known as the eternal connected vertex cover number and is denoted by the ecvc(G). The decision version of the eternal connected vertex cover problem is NP-hard for general graphs and it also remains NP-hard for bipartite graphs. In this paper, we proved that the problem is polynomial-time solvable for chain graphs and cographs. In addition, we proved that the problem is NP-hard for Hamiltonian graphs, and proposed a polynomial-time algorithm to compute eternal connected vertex cover number for Mycielskian of a given Hamiltonian graph.
The Traveling Salesman Problem is one of the most relevant challenges today, as the need to solve it arises in various fields. However, there is no clear algorithm for its solution. It falls within the realm of NP-com...
详细信息
ISBN:
(纸本)9783031782657;9783031782664
The Traveling Salesman Problem is one of the most relevant challenges today, as the need to solve it arises in various fields. However, there is no clear algorithm for its solution. It falls within the realm of NP-complete problems and is optimization-oriented. While it is assumed that the solution to these problems involves exhaustive search, in practice, various algorithms and approaches are often used to reduce the volume of analyzed solutions, aiming to find a way to solve the problem without exhaustive search. This includes methods like branch and bound to expedite the search or artificial intelligence approaches such as the ant colony algorithm and genetic algorithms to accelerate the process while achieving the closest possible solution. Genetic methods are one of the most powerful tools for solving such tasks. These algorithms model evolutionary processes, which, thanks to the basic principles of evolution, allow finding better solutions. This approach allows representing the task as a certain evolutionary process. It is based on the fact that from the very beginning, a certain set of solutions is chosen, and they start competing with each other. Each solution represents an individual, and a set of its solutions represents a "gene". Each of these genes during the algorithm's operation can evolve, adapt, or mutate according to the rules of the environment. In the end, only the strongest genes should remain, which will be the approximate optimal solution. A characteristic of these algorithms is that each implementation can be unique. An important task in building algorithms is precisely the optimization of their parameters, as well as choosing the right approach to some of its stages, where only the best of them will remain in the end. This methodology not only allows finding approximately optimal solutions but also provides flexibility and adaptability for various requirements and constraints.
Path-based testing is an established method for creating test cases comprising sequences of steps executed in a System Under Test (SUT). Several algorithms for generating the test sequences (paths) that satisfy variou...
详细信息
ISBN:
(纸本)9798350365634
Path-based testing is an established method for creating test cases comprising sequences of steps executed in a System Under Test (SUT). Several algorithms for generating the test sequences (paths) that satisfy various test coverage criteria determining their properties are published in the literature. However, existing path-based testing techniques have limited applicability in numerous practical cases, such as when executing a particular test step in the test further excludes the execution of another test step. More complex exclusion requirements (further denoted negative constraints) exist in real systems, depending on the number of executions of a particular test step. In the paper, we discuss two possible negative constraints, namely, (1) the complete exclusion of a step as a consequence of the execution of a particular previous step and (2) the requirement to include a particular step maximally once in one test path, when another step was executed previously. We present a novel ant-colony-optimization (ACO) principle-based algorithm, accepting a SUT model based and a set of negative constraints, and computing a set of test paths while maximizing edge coverage and satisfying the given set of negative constraints. We compare the results of the ACO-based algorithm with those returned by a baseline, an alternative algorithm that excludes specific test paths from a set of test paths satisfying edge coverage, and, for reference, with results returned by an algorithm that generates test paths that satisfy edge coverage. Evaluated on 152 problem instances, the presented ACO-based algorithm outperformed the baseline in the average length of test paths (representing the testing costs) lower by 32.62%. Also, the ratio of edge coverage satisfaction in the set of test paths computed by the ACO-based algorithm is better by 3.41% compared to the baseline.
This work considers the problem of output-sensitive listing of occurrences of 2k-cycles for fixed constant k ≥ 2 in an undirected host graph with m edges and t 2k-cycles. Recent work of Jin and Xu (and independently ...
详细信息
We study learning-augmented streaming algorithms for estimating the value of MAX-CUT in a graph. In the classical streaming model, while a 1/2-approximation for estimating the value of MAX-CUT can be trivially achieve...
详细信息
Vizing's theorem states that any n-vertex m-edge graph of maximum degree. can be edge colored using at most Delta + 1 different colors [Diskret. Analiz, '64]. Vizing's original proof is algorithmic and sho...
详细信息
ISBN:
(纸本)9798331516758;9798331516741
Vizing's theorem states that any n-vertex m-edge graph of maximum degree. can be edge colored using at most Delta + 1 different colors [Diskret. Analiz, '64]. Vizing's original proof is algorithmic and shows that such an edge coloring can be found in (O) over tilde (mn) time. This was subsequently improved to (O) over tilde (m root n), independently by Arjomandi [1982] and by Gabow et al. [1985]. In this paper we present an algorithm that computes such an edge coloring in (O) over tilde (mn(1/3)) time, giving the first polynomial improvement for this fundamental problem in over 40 years.
Partial domination problem is a generalization of the minimum dominating set problem on graphs. Here, instead of dominating all the nodes, one asks to dominate at least a fraction of the nodes of the given graph by ch...
详细信息
A segment-graph algorithm is provided for wireless spectrum allocation in cognitive networks based on the cooperation of the secondary users, which aim to maximize the utilization of the limited spectrum bands and min...
详细信息
A segment-graph algorithm is provided for wireless spectrum allocation in cognitive networks based on the cooperation of the secondary users, which aim to maximize the utilization of the limited spectrum bands and minimize the total cost of all the secondary users to buy (or lease) the spectrum bands. The segment-graph of the complement graph of the original interference graph is defined. The proposed segment-graph algorithm is based on finding the complete subgraph of the segment-graph repeatedly. It is proved that the proposed algorithm always obtains the optimal solution if one of the segment-graphs is complete in each iteration. In general cases, the proposed algorithm dramatically reduces the total cost of all the secondary users. Comparative simulations agree with the theoretical results obtained.
暂无评论