Fingerprint-based indoor localization methods are promising due to the high availability of deployed access points and compatibility with commercial-off-the-shelf user devices. However, to train regression models for localization, an extensive site survey is required to collect fingerprint data from the target areas. In this paper, we consider the problem of informative path planning (IPP) to find the optimal walk for site survey subject to a budget constraint. IPP for location fingerprint collection is related to the well-known orienteering problem (OP) but is more challenging due to edge-based non-additive rewards and revisits. Given the NP-hardness of IPP, we propose two heuristic approaches: a Greedy algorithm and a genetic algorithm. We show through experimental data collected from two indoor environments with different characteristics that the two algorithms have low computation complexity, can generally achieve higher utility and lower localization errors compared to the extension of two state-of-the-art approaches to OP.
Even with RG-QP, the run time is long for practical problems, especially when the number of vertices or the budget is large. As presented in the experiments in @cite_14 , even with a small graph of 16 nodes, it takes many hours or even days when the budget is large. Furthermore, the run time is sensitive to the recursion depth @math since it is exponential with respect to @math . As a result, the recursive greedy algorithm can be only used to solve the OP when the number of vertices and the budget is small.
@cite_14
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We consider the budget allocation problem over bipartite influence model proposed by (, 2012). This problem can be viewed as the well-known influence maximization problem with budget constraints. We first show that this problem and its much more general form fall into a general setting; namely the monotone submodular function maximization over integer lattice subject to a knapsack constraint. Our framework includes 's model, even with a competitor and with cost. We then give a (1 - 1 e)-approximation algorithm for this more general problem. Furthermore, when influence probabilities are nonincreasing, we obtain a faster (1 - 1 e)-approximation algorithm, which runs essentially in linear time in the number of nodes. This allows us to implement our algorithm up to almost 10M edges (indeed, our experiments tell us that we can implement our algorithm up to 1 billion edges. It would approximately take us only 500 seconds.). The greedy sequential algorithm for maximal independent set (MIS) loops over the vertices in an arbitrary order adding a vertex to the resulting set if and only if no previous neighboring vertex has been added. In this loop, as in many sequential loops, each iterate will only depend on a subset of the previous iterates (i.e. knowing that any one of a vertex's previous neighbors is in the MIS, or knowing that it has no previous neighbors, is sufficient to decide its fate one way or the other). This leads to a dependence structure among the iterates. If this structure is shallow then running the iterates in parallel while respecting the dependencies can lead to an efficient parallel implementation mimicking the sequential algorithm. In this paper, we show that for any graph, and for a random ordering of the vertices, the dependence length of the sequential greedy MIS algorithm is polylogarithmic (O(log^2 n) with high probability). Our results extend previous results that show polylogarithmic bounds only for random graphs. We show similar results for greedy maximal matching (MM). For both problems we describe simple linear-work parallel algorithms based on the approach. The algorithms allow for a smooth tradeoff between more parallelism and reduced work, but always return the same result as the sequential greedy algorithms. We present experimental results that demonstrate efficiency and the tradeoff between work and parallelism. This paper introduces a fast solution procedure to solve 100-node instances of the time-dependent orienteering problem (TD-OP) within a few seconds of computation time. Orienteering problems occur in logistic situations were an optimal combination of locations needs to be selected and the routing between the selected locations needs to be optimized. In the time-dependent variant, the travel time between two locations depends on the departure time at the first location. Next to a mathematical formulation of the TD-OP, the main contribution of this paper is the design of a fast and effective algorithm to tackle this problem. This algorithm combines the principles of an ant colony system (ACS) with a time-dependent local search procedure equipped with a local evaluation metric. Additionally, realistic benchmark instances with varying size and properties are constructed. The average score gap with the known optimal solution on these test instances is only 1.4 with an average computation time of 0.5seconds. An extensive sensitivity analysis shows that the performance of the algorithm is insensitive to small changes in its parameter settings. We study the complexity of motivating time-inconsistent agents to complete long term projects in a graph-based planning model as proposed by Kleinberg and Oreni¾?[5]. Given a task graph G with n nodes, our objective is to guide an agent towards a target node t under certain budget constraints. The crux is that the agent may change its strategy over time due to its present-bias. We consider two strategies to guide the agent. First, a single reward is placed at t and arbitrary edges can be removed from G. Secondly, rewards can be placed at arbitrary nodes of G but no edges must be deleted. In both cases we show that it is NP-complete to decide if a given budget is sufficient to guide the agent. For the first setting, we give complementing upper and lower bounds on the approximability of the minimum required budget. In particular, we devise a @math 1+n-approximation algorithm and prove NP-hardness for ratios greater than @math n 3. Finally, we argue that the second setting does not permit any efficient approximation unless @math P=NP.