Complexity of Token Swapping and its Variants

In the Token Swapping problem we are given a graph with a token placed on each vertex. Each token has exactly one destination vertex, and we try to move all the tokens to their destinations, using the minimum number of swaps, i.e., operations of exchanging the tokens on two adjacent vertices. As the main result of this paper, we show that Token Swapping is $W[1]$-hard parameterized by the length $k$ of a shortest sequence of swaps. In fact, we prove that, for any computable function $f$, it cannot be solved in time $f(k)n^{o(k / \log k)}$ where $n$ is the number of vertices of the input graph, unless the ETH fails. This lower bound almost matches the trivial $n^{O(k)}$-time algorithm. We also consider two generalizations of the Token Swapping, namely Colored Token Swapping (where the tokens have different colors and tokens of the same color are indistinguishable), and Subset Token Swapping (where each token has a set of possible destinations). To complement the hardness result, we prove that even the most general variant, Subset Token Swapping, is FPT in nowhere-dense graph classes. Finally, we consider the complexities of all three problems in very restricted classes of graphs: graphs of bounded treewidth and diameter, stars, cliques, and paths, trying to identify the borderlines between polynomial and NP-hard cases.Comment: 23 pages, 7 Figure

Reconfiguration in bounded bandwidth and treedepth

We show that several reconfiguration problems known to be PSPACE-complete remain so even when limited to graphs of bounded bandwidth. The essential step is noticing the similarity to very limited string rewriting systems, whose ability to directly simulate Turing Machines is classically known. This resolves a question posed open in [Bonsma P., 2012]. On the other hand, we show that a large class of reconfiguration problems becomes tractable on graphs of bounded treedepth, and that this result is in some sense tight.Comment: 14 page

Fault Diameter and Efficient Fault-Tolerant Routing in a Class of Alternating Group Networks

作为加利图的一种,自选图Agn相对于其它网络结构,在并行计算及分布式计算领域有着更好的特性,因而受到广泛的重视。Ann是由翼有虎提出的基于Agn的一类新的网络结构。这个新的网络结构在直径、容错度、容错直径和汉密尔顿连通性上都优于网络Agn。虽然该网络结构已经有了较好的非容错路由算法,但是依然没有一种针对这个结构的容错路由算法以完善其实际应用。文中通过研究Ann的性质,得出了容错直径,然后基于该容错直径,设计并实现了Ann容错路由算法,最后验证了该算法的正确性。Alternating group graphs AGn,as a class of Cayley graphs,received attention for that possess certain desirable properties compared with other regular networks in parallel and distributed computing.A new form of the graphs AGn which is called ANn,studied by Youhu,shows advantages over AGn.For example,the diameter,fault tolerant,fault diameter and Hamilton connectivity are better than AGn.In this paper,the exact value of the new network's fault diameter to access its robustness is found out and the first efficient fault-tolerant routing algorithm for this class of network is presented

Complexity of token swapping and its variants

AbstractIn the Token Swapping problem we are given a graph with a token placed on each vertex. Each token has exactly one destination vertex, and we try to move all the tokens to their destinations, using the minimum number of swaps, i.e., operations of exchanging the tokens on two adjacent vertices. As the main result of this paper, we show that Token Swapping is W[1]-hard parameterized by the length k of a shortest sequence of swaps. In fact, we prove that, for any computable function f, it cannot be solved in time f(k)no(k/logk) where n is the number of vertices of the input graph, unless the ETH fails. This lower bound almost matches the trivial nO(k)-time algorithm. We also consider two generalizations of the Token Swapping, namely Colored Token Swapping (where the tokens have colors and tokens of the same color are indistinguishable), and Subset Token Swapping (where each token has a set of possible destinations). To complement the hardness result, we prove that even the most general variant, Subset Token Swapping, is FPT in nowhere-dense graph classes. Finally, we consider the complexities of all three problems in very restricted classes of graphs: graphs of bounded treewidth and diameter, stars, cliques, and paths, trying to identify the borderlines between polynomial and NP-hard cases

Math-Failure Associations, Attentional Biases, and Avoidance Bias: The Relationship with Math Anxiety and Behaviour in Adolescents

Background: Math anxiety in adolescence negatively affects learning math and careers. The current study investigated whether three cognitive biases, i.e. math-failure associations, attentional biases (engagement and disengagement), and avoidance bias for math, were related to math anxiety and math behaviour (math grade and math avoidance behaviour). Methods: In total, 500 secondary school students performed three cognitive bias tasks, questionnaires and a math performance task, and reported their grades. Results: Math-failure associations showed the most consistent associations with the outcome measures. They were associated with higher math anxiety above and beyond sex and education level. Those math-failure associations were also associated with lower grades and more avoidance behaviour, however, not above and beyond math anxiety. Engagement bias and avoidance tendency bias were associated with math avoidance behaviour, though the avoidance bias finding should be interpreted with care given the low reliability of the measure. Disengagement biases were not associated with any math anxiety nor behaviour outcome measure. Conclusions: Whereas a more reliable instrument for avoidance bias is necessary for conclusions on the relations with math performance and behaviour, the current results do suggest that math-failure associations, and not attentional bias, may play a role in the maintenance of math anxiety.</p

Complexity of token swapping and its variants

AbstractIn the Token Swapping problem we are given a graph with a token placed on each vertex. Each token has exactly one destination vertex, and we try to move all the tokens to their destinations, using the minimum number of swaps, i.e., operations of exchanging the tokens on two adjacent vertices. As the main result of this paper, we show that Token Swapping is W[1]-hard parameterized by the length k of a shortest sequence of swaps. In fact, we prove that, for any computable function f, it cannot be solved in time f(k)no(k/logk) where n is the number of vertices of the input graph, unless the ETH fails. This lower bound almost matches the trivial nO(k)-time algorithm. We also consider two generalizations of the Token Swapping, namely Colored Token Swapping (where the tokens have colors and tokens of the same color are indistinguishable), and Subset Token Swapping (where each token has a set of possible destinations). To complement the hardness result, we prove that even the most general variant, Subset Token Swapping, is FPT in nowhere-dense graph classes. Finally, we consider the complexities of all three problems in very restricted classes of graphs: graphs of bounded treewidth and diameter, stars, cliques, and paths, trying to identify the borderlines between polynomial and NP-hard cases

Spacelab 3 Mission Science Review

Papers and abstracts of the presentations made at the symposium are given as the scientific report for the Spacelab 3 mission. Spacelab 3, the second flight of the National Aeronautics and Space Administration's (NASA) orbital laboratory, signified a new era of research in space. The primary objective of the mission was to conduct applications, science, and technology experiments requiring the low-gravity environment of Earth orbit and stable vehicle attitude over an extended period (e.g., 6 days) with emphasis on materials processing. The mission was launched on April 29, 1985, aboard the Space Shuttle Challenger which landed a week later on May 6. The multidisciplinary payload included 15 investigations in five scientific fields: material science, fluid dynamics, life sciences, astrophysics, and atmospheric science

Calorimetric and Dielectric Studies of Self-assembled Bio-molecules in an Aqueous Environment

Self-assembly and the induced orientation of microscopic biological systems is of great scientific interest, because it holds the promise of many pharmaceutical applications. This dissertation presents experimental studies done on proteins, short DNA fragments, and cholesterol structures self-assembled in an aqueous environment. The goal is to probe the thermo-physical properties of these systems, their phases and phase transitions, in order to better under-stand the principles behind their unique assemblies and function. It is accepted that in all these systems the solvent water plays an important role on the assembly folding, orientation, and activity of biopolymers. However, the abundance of water in typical samples presents many experimental challenges. It is indeed the case that changes in the properties of hydration in watery environments are responsible for the dynamics of protein and DNA biomolecules. We have explored in more detail the thermodynamics, the structural properties, and the dynamics near structural transitions of biomolecules in their native aqueous environment