Interpreting three-leaf binary trees or rooted triples as constraints yields an entailment relation, whereby binary trees satisfying some rooted triples must also thus satisfy others, and thence a closure operator, which is known to be polynomial-time computable. This is extended to inconsistent triple sets by defining that a triple is entailed by such a set if it is entailed by any consistent subset of it. Determining whether the closure of an inconsistent rooted triple set can be computed in polynomial time was posed as an open problem in the Isaac Newton Institute's "Phylogenetics" program in 2007. It appears (as NC4) in a collection of such open problems maintained by Mike Steel, and it is the last of that collection's five problems concerning computational complexity to have remained open. We resolve the complexity of computing this closure, proving that its decision version is NP-Complete. In the process, we also prove that detecting the existence of any acyclic B-hyperpath (from specified source to destination) is NP-Complete, in a significantly narrower special case than the version whose minimization problem was recently proven NP-hard by Ritz et al. This implies it is NP-hard to approximate (our special case of) their minimization problem to within any factor.

In this paper we study the following problem: given a set of m sensors that collectively cover a set of n target points with heterogeneous coverage requirements (target j needs to be covered every fjslots), how to schedule the sensor duty cycles such that all coverage requirements are satisfied and the maximum number of sensors turned on at any time slot is minimized. The problem models varied real-world applications in which sensing tasks exhibit high discrepancy in coverage requirements - critical locations often need to be covered much more frequently. We provide multiple algorithms with best approximation ratio of O (log n + log m) for the maximum number of sensors to turn on, and bi-criteria algorithm with (α, β)-approximation factors with high probability, where the number of sensors turned on is an α = O(δ(log (n) + log(m))/β)-approximation of the optimal (satisfying all requirements) and the coverage requirement is a β-approximation; δ is the approximation ratio achievable in an appropriate instance of set multi-cover. When the sensor coverage exhibits extra geometric properties, the approximation ratios can be further improved. We also evaluated our algorithms via simulations and experiments on a camera testbed. The performance improvement (energy saving) is substantial compared to turning on all sensors all the time, or a random scheduling baseline.

We study a lossy coding scenario, posed as an algorithmic optimization problem, where we trade off between the conflicting goals of accuracy and privacy, motivated by scenarios such as the public release of estimates of data that accurately reflect some aspects of the raw data without revealing other sensitive confidential aspects of it, or permitting it to be inferred. More precisely, given a discrete probability distribution p(D, X, Y), where X represents the whitelisted inferences from D and Y represents the blacklisted inferences, we seek to construct a conditional distribution p(M|D) with the dual goals of making I(M; X) large and I(M; Y) small. Chakraborty et al. 2013 [1] provided optimal solutions within this model to the two extreme points on the two objectives' Pareto frontier: maximizing I(M; X) subject to the constraint that I(M; Y) be as small as possible (“perfect privacy”, using linear programming (LP)) and vice versa (“perfect utility”, which is trivial). In this paper we provide a faster combinatorial optimal algorithm for the perfect privacy problem, which does not require the use of an LP solver. Moreover, this algorithm any be used to compute Pareto-optimal solutions at any point on the Pareto frontier. (En route to this algorithm, we also provide a mathematical programming-based solution.) This solves the primary open problem posed by [1].

We study the r-gather clustering problem in a mobile and distributed setting. In this problem, nodes must be clustered into groups of at least r nodes each, and the goal is to minimize the diameter of the clusters. This notion of clustering is motivated by protecting user anonymity in location-based services or trajectory publication. Prior works on r-gather problems are centralized and cannot be easily adapted to the mobile setting. We describe a distributed algorithm that produces compact clusters, within an approximation factor 4 of the minimum cluster diameter possible. The algorithm can run on the mobile nodes and access points at the network edge locally, and can handle node mobility, rapidly switching cluster memberships as needed. The distributed approach naturally comes with the advantage of greater resilience and stability. Additionally, we show that it achieves local optimality; i.e., from the point of view of any particular node, the solution is nearly as favorable as possible, irrespective of the global configuration. We also show how to cluster trajectories with dynamic re-groupings. Further, we improve the theoretical hardness results for the problem in the Euclidean setting.

Sensor networks and the Internet of Things motivate novel classes of job scheduling problems where each "job" corresponds to downloading some data object from the sensor network, i.e., querying the network for some portion of its current state. The purpose of scheduling a set of jobs may be to support decision tasks, where the user will make a choice, prior to a deadline, informed by all the data obtained about the current situation or state. Because different aspects of the state will tend to change over time, rendering previously downloaded measurements of them "stale", we want all the data jobs to be still fresh when the last one completes. This leads to scheduling constraints much more complex than simply meeting a deadline. We investigate such freshness scheduling problems under several scenarios. We give a polynomial-time optimal algorithm for the problem of maximizing the (weighted) number of jobs scheduled via a single download channel, and an O(log n)- approximation algorithm for the (NP-hard) problem of scheduling all jobs via a minimum number of channels. The optimal algorithm exploits a shared structure between (single-deadline) freshness scheduling and ordinary scheduling with jobs-specific deadlines. Finally, we compare our approximation algorithm with natural heuristics in simulation.

We consider the network-wide broadcast problem in multihop wireless networks with reliable multicast at the Medium Access Control (MAC) layer, where the cost of transmitting to downstream nodes at each branch point in the broadcast tree depends on the number$k$of recipients, specifically$1+A k^b$in our model (for some$b \geq 0$,$A \geq 0$). This allows us to capture a wide array of MAC-layer approaches and their costs, simply by varying the value of$b$(relative to$A$), in a problem formulation subsuming the Connected Dominating Set and Spanning Tree problems. We give a systematic analysis of this problem, including positive and negative results. In particular, we show the problem is: approximable by a factor varying from$2H_{\Delta}+2$down to 2 as$b$varies from 0 to 1 (where$\Delta$is the maximum degree of the network graph and$H_\Delta$is the$\Delta$th harmonic number); approximable by a factor varying from 2 to 1 (i.e., optimal) as$b$varies from 1 to$\log _2 (\frac{1}{A}+2)$; and optimally solvable thereafter. Finally, we present numerical results comparing the two algorithms above with other natural heuristics. We find there is an advantage in algorithms taking into consideration the value$b$, even if$b$can only be roughly estimated.

An important problem in the study of sensor networks is how to select a set of sensors that maximizes coverage of other sensors. Given pair wise coverage values, three commonly found functions give some estimate of the aggregate coverage possible by a set of sensors: maximum coverage by any selected sensor (MAX), total coverage by all selected sensors (SUM), and the probability of correct prediction by at least one sensor (PROB). MAX and SUM are two extremes of possible coverage, while PROB, based on an independence assumption, is in the middle. This paper addresses the following question: what guarantees can be made of coverage that is evaluated by an unknown sub-modular function of coverage when sensors are selected according to MAX, SUM, or PROB? We prove that the guarantees are very bad: In the worst case, coverage differs by a factor of sqrt(n), where n is the number of sensors. We show in simulations on synthetic and real data that the differences can be quite high as well. We show how to potentially address this problem using a hybrid of the coverage functions.

Timely and efficient message transmission through intermittently and sparsely connected networks is a problem of significant interest to the mobile networking community. Although the long-term statistics describing the time-varying connectivity in such networks can be characterized systematically and can be used for selecting good routes, it may be possible to achieve better performance by intelligently using the actual link states at the time of routing, in conjunction with these statistical dynamics models. In this paper, we investigate a family of minimum expected latency routing methods for such dynamic networks, spanning purely model-based and state-oblivious source routing, state-based source routing, and various flavors of dynamic (or hop-by-hop) routing, with increasing amounts of current link state knowledge around the source. First, we give a heuristic and an approximation scheme for the model-assisted source routing problem, as well as heuristics for the dynamic routing problem. Then we show using extensive simulations on both synthetic and real time-varying connectivity traces that although dynamically sampling link states helps to improve expected routing latency compared to source routing, the marginal improvements decline rapidly for knowledge of current link states beyond 2 hops. To the best of our knowledge, this is the first thorough characterization of the performance of the entire spectrum of model-assisted routing algorithms ranging from little knowledge to complete knowledge of link dynamics.

We study a data dissemination scenario in which data items are to be transmitted to mobile clients via one of the stationary data access points (APs) that the clients pass by en route to their destinations. The scheduler dedicates sequences of consecutive timeslots of an AP to downloading a data item to a client during the time window in which it is in range, which corresponds to assigning a job (the client's download) to a machine (the AP) among many. The transmission rate chosen for each assignment partly corresponds to setting a machine's speed, but it also has subtler effects. The APs may control transmission power to tune its transmission range making sure that no interference occurs with neighboring APs' transmissions. The problem is a generalization of an already NP-hard parallel-machine scheduling problem in which jobs' release times and deadlines depend on the machine to which they are assigned. We define this joint timeslot, power control, and rate assignment problem formally and apply both new algorithms and adaptations of existing algorithms to it. We evaluate these algorithms through simulations which show that our proposed algorithms achieve near-optimal throughput.

Support for intelligent and autonomous resource management is one key factor to the success of modern sensor network systems. The limited resources, such as exhaustible battery life, moderate processing ability and finite bandwidth, restrict the system's ability to serve multiple users simultaneously. It always happens that only a subset of tasks is selected with the goal of maximizing total profit. Besides, because of uncertain factors like unreliable wireless medium or variable quality of sensor outputs, it is not practical to assume that both demands and profits of tasks are deterministic and known a priori, both of which may be stochastic following certain distributions. In this paper, we model this resource allocation challenge as a stochastic knapsack problem. We study a specific case in which both demands and profits follow normal distributions, which are then extended to Poisson and Binomial variables. A couple of tunable parameters are introduced to configure two probabilities: one limits the capacity overflow rate with which the combined demand is allowed to exceed the available supply, and the other sets the minimum chance at which expected profit is required to be achieved. We define relative values for random variables in given conditions, and utilize them to search for the best resource allocation solutions. We propose heuristics with different optimality/efficiency tradeoffs, and find that our algorithms run relatively fast and provide results considerably close to the optimum.

Illegal extraction of forest resources is fought, in many developing countries, by patrols that try to make this activity less profitable, using the threat of confiscation. With a limited budget, officials will try to distribute the patrols throughout the forest intelligently, in order to most effectively limit extraction. Prior work in forest economics has formalized this as a Stackelberg game, one very different in character from the discrete Stackelberg problem settings previously studied in the multiagent literature. Specifically, the leader wishes to minimize the distance by which a profit-maximizing extractor will trespass into the forest---or to maximize the radius of the remaining ``pristine'' forest area. The follower's cost-benefit analysis of potential trespass distances is affected by the likelihood of being caught and suffering confiscation. In this paper, we give a near-optimal patrol allocation algorithm and a 1/2-approximation algorithm, the latter of which is more efficient and yields simpler, more practical patrol allocations. Our simulations indicate that these algorithms substantially outperform existing heuristic allocations.

We study a data dissemination scenario in which data items are to be transmitted to mobile clients via one of the stationary data access points (APs) that the clients pass by en route to their destinations. The scheduler dedicates sequences of consecutive timeslots of an AP to downloading a data item to a client during the time window in which it is in range, which corresponds to assigning a job (the client's download) to a machine (the AP) among many. The transmission rate chosen for each assignment partly corresponds to setting a machine's speed, but it also has subtler effects. The APs may control transmission power to tune its transmission range making sure that no interference occurs with neighboring APs' transmissions. The problem is a generalization of an already NP-hard parallel-machine scheduling problem in which jobs' release times and deadlines depend on the machine to which they are assigned. We define this joint timeslot, power control, and rate assignment problem formally and apply both new algorithms and adaptations of existing algorithms to it. We evaluate these algorithms through simulations which show that our proposed algorithms achieve near-optimal throughput.

In proof-of-payment transit systems, passengers are legally required to purchase tickets before entering but are not physically forced to do so. Instead, patrol units move about the transit system, inspecting the tickets of passengers, who face fines if caught fare evading. The deterrence of such fines depends on the unpredictability and effectiveness of the patrols. In this paper, we present TRUSTS, an application for scheduling randomized patrols for fare inspection in transit systems. TRUSTS models the problem of computing patrol strategies as a leader-follower Stackelberg game where the objective is to deter fare evasion and hence maximize revenue. This problem differs from previously studied Stackelberg settings in that the leader strategies must satisfy massive temporal and spatial constraints; moreover, unlike in these counterterrorism-motivated Stackelberg applications, a large fraction of the ridership might realistically consider fare evasion, and so the number of followers is potentially huge. A third key novelty in our work is deliberate simplification of leader strategies to make patrols easier to be executed. We present an efficient algorithm for computing such patrol strategies and present experimental results using real-world ridership data from the Los Angeles Metro Rail system. The Los Angeles County Sheriff’s department has begun trials of TRUSTS.

Data-gathering or convergecast problems have traditionally been studied in two combinations of settings: one-shot scheduling of data items with no aggregation, and periodic scheduling of data items with full aggregation meaning that any number of unit-size data items can, if available, be aggregated into a single (unit-size) data item (e.g., by summing or averaging values). In this paper, we extend beyond these problem settings in two ways. First, we study a) one-shot throughput maximization in settings with aggregation and b) periodic scheduling in settings without aggregation. Second, we generalize the notion of aggregatability in both one-shot and periodic scheduling beyond the binary choice of either all sets of items being aggregatable or none being so. Modeling the presence of multiple semantic data types (e.g., target counts to be summed and temperature readings to be averaged), we partition data items into classes, whereby items are aggregatable if they belong to the same class, in both periodic and non-periodic settings. For these two problems we provide guaranteed approximations and heuristics, for a variety of general and special cases. We then evaluate the algorithms in a systematic simulation study, both under the conditions in which our provable guarantees apply and in more general settings, where we find the algorithms continue to perform well on typical problem inputs.

We consider variations of a problem in which data must be delivered to mobile clients en route, as they travel toward their destinations. The data can only be delivered to the mobile clients as they pass within range of wireless base stations. Example scenarios include the delivery of building maps to firefighters responding to multiple alarms. We cast this scenario as a parallel-machine scheduling problem with the little-studied property that jobs may have different release times and deadlines when assigned to different machines. We present new algorithms and also adapt existing algorithms, for both online and offline settings. We evaluate these algorithms on a variety of problem instance types, using both synthetic and real-world data, including several geographical scenarios, and show that our algorithms produce schedules achieving near-optimal throughput.

Positioning disk-shaped sensors to optimize certain coverage parameters is a fundamental problem in ad hoc sensor networks. The hexagon lattice arrangement is known to be optimally efficient in the plane, even though 20.9% of the area is unnecessarily covered twice, however, the arrangement is very rigid—any movement of a sensor from its designated grid position (due to, e.g., placement error or obstacle avoidance) leaves some region uncovered, as would the failure of any one sensor. In this article, we consider how to arrange sensors in order to guarantee multiple coverage, that is, k -coverage for some value k > 1. A naive approach is to superimpose multiple hexagon lattices, but for robustness reasons, we may wish to space sensors evenly apart. We present two arrangement methods for k -coverage: (1) optimizing a Riesz energy function in order to evenly distribute nodes, and (2) simply shrinking the hexagon lattice and making it denser. The first method often approximates the second, and so we focus on the latter. We show that a density increase tantamount to k copies of the lattice can yield k ′-coverage, for k ′ > k (e.g., k = 11, k ′ = 12 and k = 21, k ′ = 24), by exploiting the double-coverage regions. Our examples' savings provably converge in the limit to the ≈ 20.9% maximum. We also provide analogous results for the square lattice and its ≈ 57% inefficiency (e.g., k = 3, k ′ = 4 and k =5, k ′ = 7) and show that for multi-coverage for some values of k ′, the square lattice can actually be more efficient than the hexagon lattice. We also explore other benefits of shrinking the lattice: Doing so allows all sensors to move about their intended positions independently while nonetheless guaranteeing full coverage and can also allow us to tolerate probabilistic sensor failure when providing 1-coverage or k -coverage. We conclude by construing the shrinking factor as a budget to be divided among these three benefits.

We introduce the pan and scan problem, in which cameras are configured to observe multiple target locations. This is representative example within a broad family of problems in which multiple sensing devices are deployed, each in general observing multiple targets. A camera's configuration here consists of its orientation and its zoom factor or field of view (its position is given); the quality of a target's reading by a camera depends (inversely) on both the distance and field of view. After briefly discussing an easy setting in which a target accumulates measurement quality from all cameras observing it, we move on to a more challenging setting in which for each target only the best measurement of it is counted. Although both variants admit continuous solutions, we observe that we may restrict our attention to solutions based on pinned cones. For a geometrically constrained setting, we give an optimal dynamic programming algorithm. For the unconstrained setting of this problem, we prove NP-hardness, present efficient centralized and distributed 2-approximation algorithms, and observe that a PTAS exists under certain assumptions. For a synchronized distributed setting, we give a 2-approximation protocol and a (2β)/(1 - α)-approximation protocol (for all 0 ≤ α ≤ 1 and β >; 1, though satisfying these constraints with equality will in different ways trivialize the guarantees) with the stability feature that no target's camera assignment changes more than logβ(m/α) times. We also discuss the running times of the algorithms and study the speed-ups that are possible in certain situations.

We consider the broadcasting problem in multi-radio multi-channel ad hoc networks. The objective is to minimize the total broadcast cost, where the cost can be of any form that is summable over all the transmissions (e.g., the transmission and reception energy, the price for accessing a specific channel). Our technical approach is based on a simplicial complex model that allows us to capture the broadcast nature of the wireless medium and the heterogeneity across radios and channels. Specifically, we show that broadcasting in multi-radio multi-channel ad hoc networks can be formulated as a minimum spanning problem in simplicial complexes. We establish the NP-completeness of the minimum spanning problem and propose two approximation algorithms with order-optimal performance guarantee. These two algorithms offer tradeoffs between performance and time complexity. In a broader context, this work appears to be the first that studies the minimum spanning problem in simplicial complexes and weighted minimum connected set cover problem.

We study a problem in which a single sensor is scheduled to observe sites periodically, motivated by applications in which the goal is to maintain up-to-date readings for all the observed sites. In the existing literature, it is typically assumed that the time for a sensor switching from one site to another is negligible. This may not be the case in applications such as camera surveillance of a border, however, in which the camera takes time to pan and tilt to refocus itself to a new geographical location. We formulate a problem with refocusing delay constraints. We prove the problem to be NP-hard and then study a special case in which refocusing is proportional to some Euclidian metric. We give a lower bound on the optimal cost for the scheduling problem. Finally, we provide and experimentally evaluate several heuristic algorithms, some of them based on this computed lower bound.

We introduce the pan and scan problem, in which cameras are configured to observe multiple target locations. A camera's configuration consists of its orientation and its zoom factor or field or view (its position is given); the quality of a target's reading by a camera depends (inversely) on both the distance and field of view.

When a sensor network is deployed, it is typically required to support multiple simultaneous missions. Schemes that assign sensing resources to missions thus become necessary. In this article, we formally define the sensor-mission assignment problem and discuss some of its variants. In its most general form, this problem is NP-hard. We propose algorithms for the different variants, some of which include approximation guarantees. We also propose distributed algorithms to assign sensors to missions which we adapt to include energy-awareness to extend network lifetime. Finally, we show comprehensive simulation results comparing these solutions to an upper bound on the optimal solution.

When a sensor network is deployed in the field it is typically required to support multiple simultaneous missions, which may start and finish at different times. Schemes that match sensor resources to mission demands thus become necessary. In this paper, we consider new sensor-assignment problems motivated by frugality, i.e., the conservation of resources, for both static and dynamic settings. In the most general setting, the problems we study are NP-hard even to approximate, and so we focus on heuristic algorithms that perform well in practice. In the static setting, we propose a greedy centralized solution and a more sophisticated solution that uses the Generalized Assignment Problem model and can be implemented in a distributed fashion. In what we call the dynamic setting, missions arrive over time and have different durations. For this setting, we give heuristic algorithms in which available sensors propose to nearby missions as they arrive. We find that the overall performance can be significantly improved if available sensors sometimes refuse to offer utility to missions they could help, making this decision based on the value of the mission, the sensor's remaining energy, and (if known) the remaining target lifetime of the network. Finally, we evaluate our solutions through simulations.

Positioning disk-shaped sensors to optimize certain coverage parameters is a fundamental problem in ad-hoc sensor networks. The hexagon grid lattice is known to be optimally efficient, but the 20.9% of the area covered by two sensors may be considered a waste. Furthermore, any movement of a sensor from its designated grid position or sensor failure, due to placement error or obstacle avoidance, leaves some region uncovered, as would the failure of any one sensor. We explore how shrinking the grid can help to remedy these shortcomings. First, shrinking to obtain a denser hexagonal lattice allows all sensors to move about their intended positions independently while nonetheless guaranteeing full coverage. Second, sufficiently increasing the lattice density will naturally yield k-coverage for k > 1. Moreover, we show that a density increase tantamount to fc copies of the lattice can yield k' -coverage, for kj> k (e.g. k = 11, kj= 12), through the exploitation of the double-coverage regions. Our examples' savings provably converge in the limit to the ap 20.9% maximum. We also provide analogous results for the square lattice and its ap 57% inefficiency, including k = 3, kj= 4, k = 5,kj= 7, indicating that for multi-coverage, the square lattice can actually be more efficient than the hexagon lattice. All these efficiency gains can be used to provide 1-coverage or fc-coverage even in the face of probabilistic sensor failure. We conclude by construing the shrinking factor as a budget to be divided among these three benefits.

We consider variations of a problem in which data must be delivered to mobile clients en-route, as they travel towards their destinations. The data can only be delivered to the mobile clients as they pass within range of wireless base stations. Example scenarios include the delivery of building maps to firefighters responding to multiple alarms, and the in-transit ldquoilluminationrdquo of simultaneous surface-to-air missiles. We cast this scenario as a parallel-machine scheduling problem with the little-studied property that jobs may have different release times and deadlines when assigned to different machines. We present new algorithms and also adapt existing algorithms, for both online and offline settings. We evaluate these algorithms on a variety of problem instance types, using both synthetic and real-world data, including several geographical scenarios, and show that our algorithms produce schedules achieving near-optimal throughput.

In many situations it is important to deliver information to personnel as they work in the field. We consider such a specialized content distribution application in wireless mesh networks. When a new mission arrives-for example, when an alarm for a fire is reported-data is pushed to storage nodes at the mission site where it may be retrieved locally by responding personnel (e.g., police, firefighters, paramedics, government officials, and the media). It is important that information is available at low latency, when requested or pulled by the personnel. The total latency experienced will be a combination of the push delay (if the personnel arrive at the mission site before all the data can be pushed), and the pull delay. Each delay component will in turn be a function of 1) the hop distance traveled by the data when pushed or pulled and 2) the congestion on the links. In this paper, we define algorithms and protocols that trade-off the push and pull latencies depending on the type of application. Our goal is to choose a storage node assignment minimizing the total latency-based cost. We start with a simple model in which cost is a function of distance, and then extend the model explicitly taking congestion into account. Since the problem is NP-hard to approximate, our focus is on developing efficient algorithms and distributed protocols that can be easily deployed in wireless mesh networks. In NS2 simulations, we find that our heuristic algorithms achieve on average a cost within at most 15 % of the optimum.

When a sensor network is deployed in the field, it is typically required to support multiple simultaneous missions, which may start and finish at different times. Schemes that match sensor resources to mission demands thus become necessary. In this paper, we propose centralized and distributed schemes to assign sensors to missions. We also adapt our distributed scheme to make it energy-aware to extend network lifetime. Finally, we show simulation results comparing these solutions. We find that our greedy algorithm frequently performs near-optimally and that the distributed schemes usually perform nearly as well.

An ad-hoc sensor network is composed of sensing devices which can measure or detect features of their environment, communicate with one other and possibly with other devices that perform data fusion. One of the problems motivated by ad-hoc sensor networks is to position sensors in order to maximize coverage, or equivalently to minimize the number of sensors required to cover a given area.