Min-cost Flow Problem Research Articles

A Traveler Incentive Program for Promoting Community-Based Ridesharing

Traffic congestion has become a serious issue around the globe, partly owing to single-occupancy commuter trips. Ridesharing can present a suitable alternative for serving commuter trips. However, there are several important obstacles that impede ridesharing systems from becoming a viable mode of transportation, including the lack of a guarantee for a ride back home as well as the difficulty of obtaining a critical mass of participants. This paper addresses these obstacles by introducing a traveler incentive program (TIP) to promote community-based ridesharing with a ride back home guarantee among commuters. The TIP program allocates incentives to (1) directly subsidize a select set of ridesharing rides and (2) encourage a small, carefully selected set of travelers to change their travel behavior (i.e., departure or arrival times). We formulate the underlying ride-matching problem as a budget-constrained min-cost flow problem and present a Lagrangian relaxation-based algorithm with a worst-case optimality bound to solve large-scale instances of this problem in polynomial time. We further propose a polynomial-time, budget-balanced version of the problem. Numerical experiments suggest that allocating subsidies to change travel behavior is significantly more beneficial than directly subsidizing rides. Furthermore, using a flat tax rate as low as 1% can double the system’s social welfare in the budget-balanced variant of the incentive program.

DAVINCI: online and Dynamic Adaptation of eVolvable vIrtual Network services over Cloud Infrastructures

Service function chains, or more generally, virtual network services, evolve throughout their life-cycle due to traffic fluctuations, resource usage, and the stringent requirements of the SLO (Service Level Objective) that must be fulfilled. Network operators resort to elasticity mechanisms (e.g., vertical and horizontal scaling) and migration procedures to adapt the service function chains dynamically to meet their requirements constantly. However, most state-of-the-art solutions do not evaluate the overall impact of such mechanisms on the service function chains or the resulting penalty costs (e.g., migration downtime and SLO violation). To bridge this gap, we propose DAVINCI, a decision-making tool with different adaptation policies that allows the network operator to adapt the service function chains to minimize network changes (e.g., reallocating paths and VNFs) while keeping penalty costs at their lowest level. Moreover, DAVINCI allows for the adaptations (e.g., migration, vertical and horizontal scaling) to be expressed as a set of decisions and leverages the Min Cost Flow problem to estimate migration downtime. The analytical evaluation shows that DAVINCI outperforms the existing state-of-the-art solution (NFV-PEAR) in terms of migration, traffic costs, and the overhead induced by the migration and elasticity mechanisms while significantly reducing penalty costs.

A branch-and-price algorithm for solving the single-hub feeder network design problem

In liner shipping, containers are generally transshipped in major hub ports in each region, between larger inter-region vessels and smaller feeder vessels. In this paper, we study the problem of designing the feeder vessel network, transporting containers between a regional hub and the surrounding feeder ports. The problem, as modelled, has many similarities with the split delivery vehicle routing problem, but with additional characteristics such as simultaneous pickups and deliveries and weekly departures. The problem also includes fleet sizing with a heterogeneous fleet and allows demand rejection at a penalty cost. We present a branch-and-price framework to solve the problem, where the subproblem is solved by enumerating vessel routes and subsequently assigning commodities by solving a min-cost flow problem for each commodity. The algorithm is tested on instances with up to 12 ports, which are all solved to optimality. Since the problem is similar to the liner shipping network design problem but without transshipments, we further study selected instances from the LINER-LIB instance suite. The Baltic instance is solved to proven optimality and we find the best known solution to the West Africa instance, significantly improving on what can be found in the literature.

The rank pricing problem with ties

In the Rank Pricing Problem (RPP), a firm intends to maximize its profit through the pricing of a set of products to sell. Customers are interested in purchasing at most one product among a subset of products. To do so, they are endowed with a ranked list of preferences and a budget. Their choice rule consists in purchasing the highest-ranked product in their list and whose price is below their budget. In this paper, we consider an extension of RPP, the Rank Pricing Problem with Ties (RPPT), in which we allow for indifference between products in the list of preferences of the customers. Considering the bilevel structure of the problem, this generalization differs from the RPP in that it can lead to multiple optimal solutions for the second level problems associated to the customers. In such cases, we look for pessimistic optimal solutions of the bilevel problem : the customer selects the cheapest product. We present a new three-indexed integer formulation for RPPT and introduce two resolution approaches. In the first one, we project out the customer decision variables, obtaining a reduced formulation that we then strengthen with valid inequalities from the former formulation. Alternatively, we follow a Benders decomposition approach leveraging the separability of the problem into a master problem and several subproblems. The separation problems to include the valid inequalities to the master problem dynamically are shown to reduce to min-cost flow problems. We finally carry out extensive computational experiments to assess the performance of the resolution approaches.

Prefetching and caching for minimizing service costs: Optimal and approximation strategies

Strategically prefetching data has been utilized in practice to improve caching performance. Apart from caching data items upon requests, they can be prefetched into the cache before requests actually occur. The caching and prefetching operations compete for the limited cache space, whose size is typically much smaller than the number of data items. A key question is how to design an optimal prefetching and caching policy, assuming that the future requests can be predicted to certain extend. This question is non-trivial even under an idealized assumption that the future requests are precisely known.To investigate this problem, we propose a cost-based service model. The objective is to find the optimal offline prefetching and caching policy that minimizes the accumulated cost for a given request sequence. By casting it as a min-cost flow problem, we are able to find the optimal policy for a data trace of length N in expected time O(N3∕2) via flow-based algorithms. However, this requires the entire trace for each request and cannot be applied in real time. To this end, we analytically characterize the optimal policy by obtaining an optimal cache eviction mechanism. We derive conditions under which proactive prefetching is a better choice than passive caching. Based on these insights, we propose a lightweight approximation policy that only exploits predictions in the near future. Moreover, the approximation policy can be applied in real time and processes the entire trace in O(N) expected time. We prove that the competitive ratio of the approximation policy is less than 2. Extensive simulations verify its near-optimal performance, for both heavy and light-tailed popularity distributions.

Efficient Multi-Object Tracking by Strong Associations on Temporal Window

In this paper, we present a multiple-object vehicle tracking system. We introduce a method to combine bounding boxes extracted from multiple CNNs-based detections as a light and accurate alternative to confidence-based detection methods such as non-maximum suppression and clustering approaches predicting a single bounding box. An intersection over union metric and a threshold value is proposed to determine whether a single detection or a connectivity graph between extracted bounding boxes exists. Affinity measurements are extracted from features representing bounding box geometry, appearance comparison, and changing scene properties. Then, data association is performed by solving the min-cost flow problem of the temporal windows’ affinity network. An affinity network of a directed graph associates the objects and determines whether an existing tracklet is maintained, terminated, or a new tracklet is initiated. Our model is evaluated and tested by KITTI object tracking—Car class benchmark dataset. Overall, the proposed multiple object tracking performance is ranked second according to the multiple object tracking accuracy, mostly tracked, mostly lost statistical metric values assure lower fragmentation and less than half of the captured ID-switch in comparison with respect to the method reaching at the highest multiple object tracking accuracy metric. Furthermore, the runtime is six times faster.

Practical Bounds on Optimal Caching with Variable Object Sizes

Many recent caching systems aim to improve miss ratios, but there is no good sense among practitioners of how much further miss ratios can be improved. In other words, should the systems community continue working on this problem? Currently, there is no principled answer to this question. In practice, object sizes often vary by several orders of magnitude, where computing the optimal miss ratio (OPT) is known to be NP-hard. The few known results on caching with variable object sizes provide very weak bounds and are impractical to compute on traces of realistic length. We propose a new method to compute upper and lower bounds on OPT. Our key insight is to represent caching as a min-cost flow problem, hence we call our method the flow-based offline optimal (FOO). We prove that, under simple independence assumptions, FOO's bounds become tight as the number of objects goes to infinity. Indeed, FOO's error over 10M requests of production CDN and storage traces is negligible: at most 0.3%. FOO thus reveals, for the first time, the limits of caching with variable object sizes. While FOO is very accurate, it is computationally impractical on traces with hundreds of millions of requests. We therefore extend FOO to obtain more efficient bounds on OPT, which we call practical flow-based offline optimal (PFOO). We evaluate PFOO on several full production traces and use it to compare OPT to prior online policies. This analysis shows that current caching systems are in fact still far from optimal, suffering 11--43% more cache misses than OPT, whereas the best prior offline bounds suggest that there is essentially no room for improvement.

Practical Bounds on Optimal Caching with Variable Object Sizes

Many recent caching systems aim to improve miss ratios, but there is no good sense among practitioners of how much further miss ratios can be improved. In other words, should the systems community continue working on this problem? Currently, there is no principled answer to this question. In practice, object sizes often vary by several orders of magnitude, where computing the optimal miss ratio (OPT) is known to be NP-hard. The few known results on caching with variable object sizes provide very weak bounds and are impractical to compute on traces of realistic length. We propose a new method to compute upper and lower bounds on OPT. Our key insight is to represent caching as a min-cost flow problem, hence we call our method the flow-based offline optimal (FOO). We prove that, under simple independence assumptions, FOO's bounds become tight as the number of objects goes to infinity. Indeed, FOO's error over 10M requests of production CDN and storage traces is negligible: at most 0.3%. FOO thus reveals, for the first time, the limits of caching with variable object sizes. While FOO is very accurate, it is computationally impractical on traces with hundreds of millions of requests. We therefore extend FOO to obtain more efficient bounds on OPT, which we call practical flow-based offline optimal (PFOO). We evaluate PFOO on several full production traces and use it to compare OPT to prior online policies. This analysis shows that current caching systems are in fact still far from optimal, suffering 11-43% more cache misses than OPT, whereas the best prior offline bounds suggest that there is essentially no room for improvement.

Dynamic discrete tomography

We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their x-rays. This particular particle tracking problem, with applications, e.g. in plasma physics, is the basic problem in dynamic discrete tomography. We introduce and analyze various different algorithmic models. In particular, we determine the computational complexity of the problem (and various of its relatives) and derive algorithms that can be used in practice. As a byproduct we provide new results on constrained variants of min-cost flow and matching problems.

Determining optimal sizes of bounded batches with rejection via quadratic min-cost flow

In this article, we consider a single machine scheduling problem, in which identical jobs are split into batches of bounded sizes. For each batch, it is allowed to produce less jobs than a given upper bound, that is, some jobs in a batch can be rejected, in which case a penalty is paid for each rejected job. The objective function is the sum of several components, including the sum of the completion times, total delivery cost, and total rejection cost. We reduce this problem to a min-cost flow problem with a convex quadratic function and adapt Tamir's algorithm for its solution.© 2017 Wiley Periodicals, Inc. Naval Research Logistics, 2017

Towards enhancing the last-mile delivery: An effective crowd-tasking model with scalable solutions

In urban logistics, the last-mile delivery from the warehouse to the consumer’s home has become more and more challenging with the continuous growth of E-commerce. It requires elaborate planning and scheduling to minimize the global traveling cost, but often results in unattended delivery as most consumers are away from home. In this paper, we propose an effective large-scale mobile crowd-tasking model in which a large pool of citizen workers are used to perform the last-mile delivery. To efficiently solve the model, we formulate it as a network min-cost flow problem and propose various pruning techniques that can dramatically reduce the network size. Comprehensive experiments were conducted with Singapore and Beijing datasets. The results show that our solution can support real-time delivery optimization in the large-scale mobile crowd-sourcing problem.

Integrating train scheduling and delay management in real-time railway traffic control

Optimization models for railway traffic rescheduling tackle the problem of determining, in real-time, control actions to reducing the effect of disturbances in railway systems. In this field, mainly two research streams can be identified. On the one hand, train scheduling models are designed to include all conditions relevant to feasible and efficient operation of rail services, from the viewpoint of operations managers. On the other hand, delay management models focus on the impact of rescheduling decisions on the quality of service perceived by the passengers. Models in the first stream are mainly microscopic, while models in the second stream are mainly macroscopic.This paper aims at merging these two streams of research by developing microscopic passenger-centric models, solution algorithms and lower bounds. Several fast heuristic methods are proposed, based on alternative decompositions of the model. A lower bound is proposed, consisting of the resolution of a set of min-cost flow problems with activation constraints. Computational experiments, based on multiple test cases of the real-world Dutch railway network, show that good quality solutions and lower bounds can be found within a limited computation time.

Minimum-Cost Network Design with (Dis)economies of Scale

Given a network, a set of demands, and a cost function $f(\cdot)$, the min-cost network design problem is to route all demands with the objective of minimizing $\sum_e f(\ell_e)$, where $\ell_e$ is the total traffic load under the routing. We focus on cost functions of the form $f(x)= \sigma + x^{\alpha}$ for $x > 0$, with $f(0) = 0$. For $\alpha \le 1$, $f(\cdot)$ is subadditive. This case corresponds to the well-studied buy-at-bulk network design problem and admits polylogarithmic approximation and hardness. In this paper, we focus on the less-studied scenario of $\alpha > 1$ with a positive start-up cost $\sigma > 0$. Now, the cost function $f(\cdot)$ is neither subadditive nor superadditive. It aims to model a range of computing and communication devices for which doubling processing speed more than doubles their power consumption. We begin by discussing why existing routing techniques such as randomized rounding and tree-metric embedding fail to generalize directly. We then present our main contribution, which is a polylogarithmic approximation algorithm. We obtain this result by first deriving a bicriteria approximation for a related capacitated min-cost flow problem that we believe is interesting in its own right. Our approach for this problem builds upon the well-linked decomposition due to Chekuri, Khanna, and Shepherd [Proceedings of ACM STOC, ACM, New York, pp. 183--192], the construction of expanders via matchings due to Khandekar, Rao, and Vazirani [J. ACM, 56 (2009), 19], and edge-disjoint routing in well-connected graphs due to Rao and Zhou [SIAM J. Comput., 39 (2010), pp. 1856--1887]. However, we also develop new techniques that allow us to keep a handle on the total cost, which was not a concern in the aforementioned literature.

Automatic tracking of vessel-like structures from a single starting point

The identification of vascular networks is an important topic in the medical image analysis community. While most methods focus on single vessel tracking, the few solutions that exist for tracking complete vascular networks are usually computationally intensive and require a lot of user interaction. In this paper we present a method to track full vascular networks iteratively using a single starting point. Our approach is based on a cloud of sampling points distributed over concentric spherical layers. We also proposed a vessel model and a metric of how well a sample point fits this model. Then, we implement the network tracking as a min-cost flow problem, and propose a novel optimization scheme to iteratively track the vessel structure by inherently handling bifurcations and paths. The method was tested using both synthetic and real images. On the 9 different data-sets of synthetic blood vessels, we achieved maximum accuracies of more than 98%. We further use the synthetic data-set to analyze the sensibility of our method to parameter setting, showing the robustness of the proposed algorithm. For real images, we used coronary, carotid and pulmonary data to segment vascular structures and present the visual results. Still for real images, we present numerical and visual results for networks of nerve fibers in the olfactory system. Further visual results also show the potential of our approach for identifying vascular networks topologies. The presented method delivers good results for the several different datasets tested and have potential for segmenting vessel-like structures. Also, the topology information, inherently extracted, can be used for further analysis to computed aided diagnosis and surgical planning. Finally, the method's modular aspect holds potential for problem-oriented adjustments and improvements.

Multiple People Tracking Using Camera Networks with Overlapping Views

We present a novel framework for multiple pedestrian tracking using overlapping cameras in which the problems of object detection and data association are solved alternately. In each round of our algorithm, the people are detected by inference on a factor graph model at each time slice. The outputs of the inference, namely, the probabilistic occupancy maps, are used to define a cost network model. Data association is achieved by solving a min-cost flow problem on the resulting network model. The outputs of the data association, namely, the ground occupancy maps, are used to control the size of factors in graph model in the next round. By alternating between object detection and data association, a desirable compromise between complexity and accuracy is obtained. Experiments results on public datasets demonstrate the competitiveness of our method compared with other state-of-the-art approaches.

Efficient Iterative Auctions for Multi-Featured Items: A Network Flow Approach

We develop a methodology for the design of efficient iterative auctions for heterogeneous items whose values are expressed in terms of a finite set of features they possess. Bidders have decreasing marginal values for each feature, and their value for a bundle is the sum of individual feature valuations associated with this bundle. This feature-driven representation of valuations allows us to formulate a novel (multicommodity) network flow representation of the efficient allocation problem. Using the integrality of the optimal solutions to the min-cost flow problem, we establish the existence of a Walrasian equilibrium for F-feature valuations (first with F = 2, and subsequently with F > 2 under additional structural assumptions). We also show that F-feature valuations might not exhibit substitutability even for F = 2, thereby revealing a new class of valuations for which a Walrasian equilibrium exists. By analyzing the structural properties of the optimal solutions to the network flow problem for 2-feature valuations, we develop an iterative algorithm that finds the efficient allocation in this setting. Furthermore, a single run of the procedure collects sufficient information to compute VCG payments. Thus, complementing the algorithm with this payment rule, we obtain a new iterative auction in which it is an (ex-post) equilibrium to bid truthfully, and the equilibrium is efficient. Our approach suggests that analyzing (i) alternative valuation representations, and (ii) network flow formulation of the efficient allocation problem, could potentially reveal other valuation classes for which a Walrasian equilibrium exists, and simple iterative auctions which implement an efficient outcome.

A Novel Framework for Multiple People Tracking Using Camera Networks with Overlapping Views

We present a novel framework for multiple pedestrian tracking using overlapping cameras in which the problems of object detection and data association are solved alternately. In each round of our algorithm, the people are detected by inference on a factor graph model at each time slice. The outputs of the inference, namely the probabilistic occupancy maps, are used to define a cost network model. Data association is achieved by solving a min-cost flow problem on the resulting network model. The outputs of the data association, namely the ground occupancy maps, are used to control the size of factors in graph model in the next round. By alternating between object detection and data association, a desirable compromise between complexity and accuracy is obtained. Our experiments involve challenging, notably distinct datasets and demonstrate that our method is competitive compared with other state-of-art approaches.

Optimal Rate Allocation for ISP-friendly P2P VoD Systems

The rapid growth of Peer-to-Peer (P2P) Video-on-Demand (VoD) applications has posed significant pressure on both content providers and Internet Service Providers (ISPs). In this paper, we focus on rate allocation algorithms which not only improve the streaming performance of P2P VoD systems but also cut down on inter-ISP traffic. We first propose two centralized rate allocation algorithms which serve as the benchmarks: one is Server-First Optimal ( SFO ) algorithm that takes minimum server load as the first order objective, and the other is Locality-First Optimal ( LFO ) algorithm that takes minimum inter-ISP traffic as the first order objective. By introducing network flow theory, SFO and LFO can be solved as a series of maximum or min-cost flow problems. Then we propose a distributed rate allocation algorithm which utilizes a novel hybrid neighbor selection strategy and models the design goals as a multi-objective optimization problem. Through simulation studies, we show that our algorithms substantially outperform traditional and state-of-the-art approaches.

Exploring a QoS driven scheduling approach for peer-to-peer live streaming systems with network coding.

Most large-scale peer-to-peer (P2P) live streaming systems use mesh to organize peers and leverage pull scheduling to transmit packets for providing robustness in dynamic environment. The pull scheduling brings large packet delay. Network coding makes the push scheduling feasible in mesh P2P live streaming and improves the efficiency. However, it may also introduce some extra delays and coding computational overhead. To improve the packet delay, streaming quality, and coding overhead, in this paper are as follows. we propose a QoS driven push scheduling approach. The main contributions of this paper are: (i) We introduce a new network coding method to increase the content diversity and reduce the complexity of scheduling; (ii) we formulate the push scheduling as an optimization problem and transform it to a min-cost flow problem for solving it in polynomial time; (iii) we propose a push scheduling algorithm to reduce the coding overhead and do extensive experiments to validate the effectiveness of our approach. Compared with previous approaches, the simulation results demonstrate that packet delay, continuity index, and coding ratio of our system can be significantly improved, especially in dynamic environments.

An O(n log n) algorithm for a single-item capacitated lot-sizing problem with linear costs and no backlogging

For the single-item capacitated lot-sizing problem with linear costs and no backlogging, we suggest a straightforward time algorithm, which does not need a polymatroid or min-cost flow problem reformulation.