The advance of tour recommendation allows people to get well-fit route plans, which contain a sequence of Points of Interest (POIs) based on tourists’ constraints and preferences. Large-scale POIs, called Super-POIs in this article, often contain multiple scenic spots and entrances. Tourists have to specify a suitable tour route inside Super-POI to obtain good tour experience. However, most of existing tour recommendation algorithms ignore the detailed information inside Super-POIs. By taking super-POIs into account, we proposeEmbedded Tour(eTOUR), a two-layer framework considering route design of POIs (Outer Model) and scenic routes inside the Super-POIs (Inner Model) respectively. To combine two models, an Embedded GRASP-VNS Algorithm is introduced based on an embedding strategy. For Outer Model, we apply Greedy Randomized Adaptive Search Procedure (GRASP) for route construction and Variable Neighborhood Search (VNS) for local improvement. Super-POI is treated as a “meta node” in outer route construction. For Inner Model, the optimal route inside Super-POI obtained by DFS-based Tree Search with Pruning is revised dynamically to adapt to the outer route. Furthermore, we discuss a special case in the Super-POI where a key graph is defined and treated as the “must go” route. We modify the solution of Chinese Postman Problem in this case to reduce the time complexity. Finally, experiments based on two real datasets demonstrate the effectiveness of our proposal.

In this paper, we consider the problem how to interconnect an obtained d-hop MIS into a d-hop CDS. Firstly, we deal with a simple case d = 2 and present a greedy algorithm. Using this method, we can obtain a 2-hop CDS with approximation ratio min{3β,2β+2+2H (β-1)}, where β is the ratio of 2-hop MIS with 2-hop CDS and H (·) is the harmonic function. This ratio is better than the ratio using spanning tree method. Finally, we generalize the algorithm for general case.

In this paper, we study the problem of computing quality fault-tolerant virtual backbone in homogeneous wireless network, which is defined as the$k$-connected$m$-dominating set problem in a unit disk graph. This problem is NP-hard, and thus many efforts have been made to find a constant factor approximation algorithm for it, but never succeeded so far with arbitrary$k\geq 3$and$m\geq 1$pair. We propose a new strategy for computing a smaller-size 3-connected$m$-dominating set in a unit disk graph with any$m\geq 1$. We show the approximation ratio of our algorithm is constant and its running time is polynomial. We also conduct a simulation to examine the average performance of our algorithm. Our result implies that while there exists a constant factor approximation algorithm for the$k$-connected$m$-dominating set problem with arbitrary$k\leq 3$and$m\geq 1$pair, the$k$-connected$m$-dominating set problem is still open with$k>3$.

In this paper, we study the problem of constructing quality fault-tolerant Connected Dominating Sets (CDSs)in homogeneous wireless networks, which can be defined as minimum k-Connected m-Dominating Set ((k,m)-CDS) problem in Unit Disk Graphs (UDGs). We found that every existing approximation algorithm for this problem is incomplete for k ¿3 in a sense that it does not generate a feasible solution in some UDGs. Based on these observations, we propose a new polynomial time approximation algorithm for computing (3,m)-CDSs. We also show that our algorithm is correct and its approximation ratio is a constant.

A Virtual Backbone (VB) of a wireless network is a subset of nodes such that only VB nodes are responsible for routing-related tasks. Since a smaller VB causes less overhead, size is the primary quality factor of VB. Frequently, Unit Disk Graphs (UDGs) are used to model 2D homogeneous wireless networks, and the problem of finding minimum VBs in the networks is abstracted as Minimum Connected Dominating Set (MCDS) problem in UDGs. In some applications, the altitude of nodes can be hugely different and UDG cannot abstract the networks accurately. Then, Unit Ball Graph (UBG) can replace UDG. In this paper, we study how to construct quality CDSs in UBGs in distributed environments. We first give an improved upper bound of the number of independent nodes in a UBG, and use this result to analyze the Performance Ratio (PR) of our new centralized algorithm C-CDS-UBG, which computes CDSs in UBGs. Next, we propose a distributed algorithm D-CDS-UBG originated from C-CDS-UBG and analyze its message and time complexities. Our theoretical analysis shows that the PR of D-CDS-UBG is 14.937, which is better than current best, 22. Our simulations also show that D-CDS-UBG outperforms the competitor, on average.