The multiperiodic crowd tracking (MPCT) problem is an extension of the periodic crowd tracking (PCT) problem, recently addressed in the literature and solved using an iterative solver called PCTs solver. For a given crowded event, the MPCT consists of follow-up crowds, using unmanned aerial vehicles (UAVs) during different periods in a life-cycle of an open crowded area (OCA). Our main motivation is to remedy an important limitation of the PCTs solver called “PCTs solver myopia” which is, in certain cases, unable to manage the fleet of UAVs to cover all the periods of a given OCA life-cycle during a crowded event. The behavior of crowds can be predicted using machine learning techniques. Based on this assumption, we proposed a new mixed integer linear programming (MILP) model, called MILP-MPCT, to solve the MPCT. The MILP-MPCT was designed using linear programming technique to build two objective functions that minimize the total time and energy consumed by UAVs under a set of constraints related to the MPCT problem. In order to validate the MILP-MPCT, we simulated it using IBM-ILOG-CPLEX optimization framework. Thanks to the “clairvoyance” of the proposed MILP-MPCT model, experimental investigations show that the MILP-MPCT model provides strategic moves of UAVs between charging stations (CSs) and crowds to provide better solutions than those reported in the literature.

Background Real biological and social data is increasingly being represented as graphs. Pattern-mining-based graph learning and analysis techniques report meaningful biological subnetworks that elucidate important interactions among entities. At the backbone of these algorithms is the enumeration of pattern space. Results We propose an efficient algorithm for enumerating all connected induced subgraphs of an undirected graph. Building on this enumeration approach, we propose an algorithm for mining all maximal cohesive subgraphs that integrates vertices’ attributes with subgraph enumeration. To efficiently mine all maximal cohesive subgraphs, we propose two pruning techniques that remove futile search nodes in the enumeration tree. Conclusions Experiments on synthetic and real graphs show the effectiveness of the proposed algorithm and the pruning techniques. On enumerating all connected induced subgraphs, our algorithm is several times faster than existing approaches. On dense graphs, the proposed approach is at least an order of magnitude faster than the best existing algorithm. Experiments on protein-protein interaction network with cancer gene dysregulation profile show that the reported cohesive subnetworks are biologically interesting.

We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al. (WINE 2013) to model the impact of asymmetric information on the revenue of the seller in take-it-or-leave-it sales. Instances of the problem consist of an $n \times m$ binary matrix $A$ and a probability distribution over its columns. A partition scheme $B=(B_1,...,B_n)$ consists of a partition $B_i$ for each row $i$ of $A$. The partition $B_i$ acts as a smoothing operator on row $i$ that distributes the expected value of each partition subset proportionally to all its entries. Given a scheme $B$ that induces a smooth matrix $A^B$, the partition value is the expected maximum column entry of $A^B$. The objective is to find a partition scheme such that the resulting partition value is maximized. We present a $9/10$-approximation algorithm for the case where the probability distribution is uniform and a $(1-1/e)$-approximation algorithm for non-uniform distributions, significantly improving results of Alon et al. Although our first algorithm is combinatorial (and very simple), the analysis is based on linear programming and duality arguments. In our second result we exploit a nice relation of the problem to submodular welfare maximization.

High dynamic range (HDR) images contain more details of the scene as compared to commonly used low dynamic range (LDR) images. The additional information in the HDR images is important for applications such as high-quality graphics rendering, sensing, scene analysis, and surveillance etc. Moreover, HDR images would provide better visualization experience on HDR displays, which might become more common in near future. Therefore, it is important to encode the entire dynamic range of the HDR images. In this paper, a new lossless, four-channel, eight bits per channel, format for encoding floating-point HDR images is proposed. The format is similar to the well-known RGBE format but constructs the E channel differently for better accuracy. Experimental results show that our technique could reduce the rounding error of the RGBE by more than 88%. In addition, there was a reduction of 44.3% in average error for all 33 images in the database used for this study.

High-dynamic-range (HDR) images require tone mapping to be displayed properly on lower dynamic range devices. In this paper, a tone-mapping algorithm that uses histogram of luminance to construct a lookup table (LUT) for tone mapping is presented. Characteristics of the human visual system (HVS) are used to give more importance to visually distinguishable intensities while constructing the histogram bins. The method begins with constructing a histogram of the luminance channel, using bins that are perceived to be uniformly spaced by the HVS. Next, a refinement step is used, which removes the pixels from the bins that are indistinguishable by the HVS. Finally, the available display levels are distributed among the bins proportionate to the pixels counts thus giving due consideration to the visual contribution of each bin in the image. Quality assessment using both quantitative evaluations and user studies suggests that the presented algorithm produces tone-mapped images that are visually pleasant and preserve details of the original image better than the existing methods. Finally, implementation details of the algorithm on GPU for parallel processing are presented, which could achieve a significant gain in speed over CPU-based implementation.

We investigate the problem of scheduling the maintenance of edges in a network, motivated by the goal of minimizing outages in transportation or telecommunication networks. We focus on maintaining connectivity between two nodes over time; for the special case of path networks, this is related to the problem of minimizing the busy time of machines. We show that the problem can be solved in polynomial time in arbitrary networks if preemption is allowed. If preemption is restricted to integral time points, the problem is NP-hard and in the non-preemptive case we give strong non-approximability results. Furthermore, we give tight bounds on the power of preemption, that is, the maximum ratio of the values of non-preemptive and preemptive optimal solutions. Interestingly, the preemptive and the non-preemptive problem can be solved efficiently on paths, whereas we show that mixing both leads to a weakly NP-hard problem that allows for a simple 2-approximation.

We consider the following machine scheduling game. Jobs, controlled by selfish players, are to be assigned to unrelated machines. A player cares only about the finishing time of his job(s), while disregarding the welfare of other players. The outcome of such games is measured by the makespan. Our goal is to design coordination mechanisms to schedule the jobs so as to minimize the price of anarchy.We introduce oligopolistic players. Each such player controls a set of jobs, with the aim of minimizing the sum of the completion times of his jobs. Our model of oligopolistic players is a natural generalization of the conventional model, where each player controls only a single job.In our setting, previous mechanisms designed for players with single jobs are inadequate, e.g., having large price of anarchy, or not guaranteeing pure Nash equilibria. To meet this challenge, we design three mechanisms that are adapted/generalized from Caragiannis' ACOORD. All our mechanisms induce pure Nash equilibria while guaranteeing relatively small price of anarchy.

Imagine a wooden plate with a set of non-overlapping geometric objects painted on it. How many of them can a carpenter cut out using a panel saw making guillotine cuts, i.e., only moving forward through the material along a straight line until it is split into two pieces? Already fifteen years ago, Pach and Tardos investigated whether one can always cut out a constant fraction if all objects are axis-parallel rectangles. However, even for the case of axis-parallel squares this question is still open. In this paper, we answer the latter affirmatively. Our result is constructive and holds even in a more general setting where the squares have weights and the goal is to save as much weight as possible. We further show that when solving the more general question for rectangles affirmatively with only axis-parallel cuts, this would yield a combinatorial O(1)-approximation algorithm for the Maximum Independent Set of Rectangles problem, and would thus solve a long-standing open problem. In practical applications, like the mentioned carpentry and many other settings, we can usually place the items freely that we want to cut out, which gives rise to the two-dimensional guillotine knapsack problem: Given a collection of axis-parallel rectangles without presumed coordinates, our goal is to place as many of them as possible in a square-shaped knapsack respecting the constraint that the placed objects can be separated by a sequence of guillotine cuts. Our main result for this problem is a quasi-PTAS, assuming the input data to be quasi-polynomially bounded integers. This factor matches the best known (quasi-polynomial time) result for (non-guillotine) two-dimensional knapsack.

We investigate coordination mechanisms that schedule n jobs on m unrelated machines. The objective is to minimize the makespan. It was raised as an open question whether it is possible to design a coordination mechanism that has constant price of anarchy using preemption. We give a negative answer. Next we introduce multi-job players that control a set of jobs, with the aim of minimizing the sum of the completion times of theirs jobs. In this setting, previous mechanisms designed for players with single jobs are inadequate, e.g., having large price of anarchy, or not guaranteeing pure Nash equilibria. To meet this challenge, we design three mechanisms that induce pure Nash equilibria while guaranteeing relatively small price of anarchy. Then we consider multi-job players where each player’s objective is to minimize the weighted sum of completion time of her jobs, while the social cost is the sum of players’ costs. We first prove that if machines order jobs according to Smith-rule, then the coordination ratio is at most 4, moreover this is best possible among non-preemptive policies. Then we design a preemptive policy, externality that has coordination ratio 2.618, and complement this result by proving that this ratio is best possible even if we allow for randomization or full information. An interesting consequence of our results is that an e−local optima of R| | ∑ wiCi for the jump neighborhood can be found in polynomial time and is within a factor of 2.618 of the optimal solution.

We consider the unrelated machine scheduling game in which players control subsets of jobs. Each player's objective is to minimize the weighted sum of completion time of her jobs, while the social cost is the sum of players' costs. The goal is to design simple processing policies in the machines with small coordination ratio, i.e., the implied equilibria are within a small factor of the optimal schedule. We work with a weaker equilibrium concept that includes that of Nash. We first prove that if machines order jobs according to their processing time to weight ratio, a.k.a. Smith-rule, then the coordination ratio is at most 4, moreover this is best possible among nonpreemptive policies. Then we establish our main result. We design a preemptive policy, externality, that extends Smith-rule by adding extra delays on the jobs accounting for the negative externality they impose on other players. For this policy we prove that the coordination ratio is 1 + φ ≈ 2.618, and complement this result by proving that this ratio is best possible even if we allow for randomization or full information. Finally, we establish that this externality policy induces a potential game and that an ε-equilibrium can be found in polynomial time. An interesting consequence of our results is that an ε −local optima of R| | ∑ w j C j for the jump (a.k.a. move) neighborhood can be found in polynomial time and are within a factor of 2.618 of the optimal solution. The latter constitutes the first direct application of purely game-theoretic ideas to the analysis of a well studied local search heuristic.

We investigate coordination mechanisms that schedule n jobs on m unrelated machines. The objective is to minimize the latest completion of all jobs, i.e., the makespan. It is known that if the mechanism is non-preemptive, the price of anarchy is Ω(logm). Both Azar, Jain, and Mirrokni (SODA 2008) and Caragiannis (SODA 2009) raised the question whether it is possible to design a coordination mechanism that has constant price of anarchy using preemption. We give a negative answer. All deterministic coordination mechanisms, if they are symmetric and satisfy the property of independence of irrelevant alternatives, even with preemption, have the price of anarchy . Moreover, all randomized coordination mechanisms, if they are symmetric and unbiased, even with preemption, have similarly the price of anarchy . Our lower bound complements the result of Caragiannis, whose bcoord mechanism guarantees O(log m/loglog m) price of anarchy. Our lower bound construction is surprisingly simple. En route we prove a Ramsey-type graph theorem, which can be of independent interest. On the positive side, we observe that our lower bound construction critically uses the fact that the inefficiency of a job on a machine can be unbounded. If, on the other hand, the inefficiency is not unbounded, we demonstrate that it is possible to break the Ω(log m/loglog m) barrier on the price of anarchy by using known coordination mechanisms.