Linear Programming Based Near-Optimal Pricing for Laminar Bayesian Online Selection

We present a framework for obtaining fully polynomial time approximation schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone single-period cost functions. This framework is developed through the establishment of two sets of computational rules, namely, the calculus of $K$-approximation functions and the calculus of $K$-approximation sets. Using our framework, we provide the first FPTASs for several NP-hard problems in various fields of research such as knapsack models, logistics, operations management, economics, and mathematical finance. Extensions of our framework via the use of the newly established computational rules are also discussed.

Discrete Choice Models and Applications in Operations Management

This paper discusses the development of strategic information systems (SIS) and examines the impact of SIS applications in operations management on sustaining organisational competitiveness. It reviews the methodology, the process and the critical parameters and factors of SIS development. A management model for SIS development that integrates various perspectives of competitive advantage, business strategy, information technology (IT) and information systems (IS) is proposed. The purposes of this paper are to review the state of published SIS research, and develop a management model that identifies a five-stage SIS development process. In synthesising SIS planning methodologies advocated in literature, the paper also elaborates an implementation guideline accompanying the proposed model.

Comparative study of the Causal Matrix and Causal Determinant

We present an efficient polynomial-time approximation scheme (EPTAS) for the problem of scheduling jobs on parallel uniform machines that improves all previously known EPTAS for the problem. Our algorithm uses a Mixed Integer Linear Program (MILP) formulation for a relaxed version of the problem. We simplify the MILP by repeatedly removing carefully selected sets of jobs and machines until all integer variables have been removed. Then, we build up the solution through the use of a dynamic programming approach, enumeration, and linear program solving. Notable about our approach is that our algorithm only uses an LP solver, different from previous EPTAS approaches where MILP solvers are necessary.

Contributors

We propose a computationally efficient fully polynomial-time approximation scheme (FPTAS) to compute an approximation with arbitrary precision of the value function of convex stochastic dynamic programs, using the technique of $K$-approximation sets and functions introduced by Halman et al. [Math. Oper. Res., 34, (2009), pp. 674--685]. This paper deals with the convex case only, and it has the following contributions. First, we improve on the worst-case running time given by Halman et al. Second, we design and implement an FPTAS with excellent computational performance and show that it is faster than an exact algorithm even for small problem instances and small approximation factors, becoming orders of magnitude faster as the problem size increases. Third, we show that with careful algorithm design, the errors introduced by floating point computations can be bounded, so that we can provide a guarantee on the approximation factor over an exact infinite-precision solution. We provide an extensive computational evaluation based on randomly generated problem instances coming from applications in supply chain management and finance. The running time of the FPTAS is both theoretically and experimentally linear in the size of the uncertainty set.

We consider two variants of the classical bin packing problem in which items may be fragmented. This can potentially reduce the total number of bins needed for packing the instance. However, since fragmentation incurs overhead, we attempt to avoid it as much as possible. In bin packing with size increasing fragmentation (BP-SIF), fragmenting an item increases the input size (due to a header/footer of fixed size that is added to each fragment). In bin packing with size preserving fragmentation (BP-SPF), there is a bound on the total number of fragmented items. These two variants of bin packing capture many practical scenarios, including message transmission in community TV networks, VLSI circuit design and preemptive scheduling on parallel machines with setup times/setup costs.While both BP-SPF and BP-SIF do not belong to the class of problems that admit a polynomial time approximation scheme (PTAS), we show in this paper that both problems admit a dual PTAS and an asymptotic PTAS. We also develop for each of the problems a dual asymptotic fully polynomial time approximation scheme (AFPTAS). The AFPTASs are based on a non-trivial application of a fast combinatorial FPTAS for packing linear programs with negative entries, proposed recently by Garg and Khandekar [5].KeywordsApproximation SchemeParallel MachinePolynomial Time Approximation SchemeLarge ItemSmall ItemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We study the Provision-after-Wait problem in healthcare introduced by Braverman, Chen, and Kannan (2016). In this setting, patients seek a medical procedure, and the procedure can be performed by different hospitals of different costs. Each patient has a value for each hospital, and a budget-constrained government/planner pays for the medical expenses of the patients. The planner's goal is to find an optimal stable assignment that is envy-free and maximizes the social welfare while keeping the expenses within the budget. In this work, we focus on the settings where the patients have a common preference of the hospitals. We show that computing the optimal stable assignment for maximizing social welfare is NP-hard. Furthermore, we construct a fully polynomial-time approximation scheme (FPTAS) that runs in time O((n+m)n3mε), where m and n are the number of hospitals and patients, respectively. In order to develop the FPTAS, we have defined and studied a new problem, ordered Knapsack. We also consider the setting where the planner uses lottery as a rationing tool. For a large sub-class of our settings, we show the conditions under which the optimal lottery scheme has a simple structure and generates more social welfare than the optimal stable assignment. Moreover, such optimal lottery scheme can be computed by a linear program.

Revenue-Sharing Allocation Strategies for Two-Sided Media Platforms: Pro-Rata versus User-Centric

In supply chain management and other operations management applications, various discrete convexities are important tools in modeling complementary or supplementary behaviors. Furthermore, the discrete nature of many decision scenarios also requires optimization tools from discrete convex theory.

We give a polynomial time approximation scheme (PTAS) for computing the supremum of a Gaussian process. That is, given a finite set of vectors $V\subseteq\mathbb{R}^d$, we compute a $(1+\varepsilon)$-factor approximation to $\mathop {\mathbb{E}}_{X\leftarrow\mathcal{N}^d}[\sup_{v\in V}|\langle v,X\rangle|]$ deterministically in time $\operatorname {poly}(d)\cdot|V|^{O_{\varepsilon}(1)}$. Previously, only a constant factor deterministic polynomial time approximation algorithm was known due to the work of Ding, Lee and Peres [Ann. of Math. (2) 175 (2012) 1409-1471]. This answers an open question of Lee (2010) and Ding [Ann. Probab. 42 (2014) 464-496]. The study of supremum of Gaussian processes is of considerable importance in probability with applications in functional analysis, convex geometry, and in light of the recent breakthrough work of Ding, Lee and Peres [Ann. of Math. (2) 175 (2012) 1409-1471], to random walks on finite graphs. As such our result could be of use elsewhere. In particular, combining with the work of Ding [Ann. Probab. 42 (2014) 464-496], our result yields a PTAS for computing the cover time of bounded-degree graphs. Previously, such algorithms were known only for trees. Along the way, we also give an explicit oblivious estimator for semi-norms in Gaussian space with optimal query complexity. Our algorithm and its analysis are elementary in nature, using two classical comparison inequalities, Slepian's lemma and Kanter's lemma.

Barrier coverage, as one of the most important applications of wireless sensor network (WSNs), is to provide coverage for the boundary of a target region. We study the barrier coverage problem by using a set of n sensors with adjustable coverage radii deployed along a line interval or circle. Our goal is to determine a range assignment $$\mathbf {R}=({r_{1}},{r_{2}}, \ldots , {r_{n}})$$ of sensors such that the line interval or circle is fully covered and its total cost $$C(\mathbf {R})=\sum _{i=1}^n {r_{i}}^\alpha $$ is minimized. For the line interval case, we formulate the barrier coverage problem of line-based offsets deployment, and present two approximation algorithms to solve it. One is an approximation algorithm of ratio 4 / 3 runs in $$O(n^{2})$$ time, while the other is a fully polynomial time approximation scheme (FPTAS) of computational complexity $$O(\frac{n^{2}}{\epsilon })$$ . For the circle case, we optimally solve it when $$\alpha = 1$$ and present a $$2(\frac{\pi }{2})^\alpha $$ -approximation algorithm when $$\alpha > 1$$ . Besides, we propose an integer linear programming (ILP) to minimize the total cost of the barrier coverage problem such that each point of the line interval is covered by at least k sensors.

Cyber deception has great potential in thwarting cyberattacks [1, 4, 8]. A defender (e.g., network administrator) can use deceptive cyber artifacts such as honeypots and faking services to confuse attackers (e.g., hackers) and thus reduce the success rate and effectiveness of attacks. However, the attackers are often diverse and some attackers may be aware of the deception and adapt to the defender's strategy. Therefore, when the defender designs the deception strategy, he needs to take into account the attacker's strategic response. Game theory is suitable for such strategic interaction between the defender and the attacker. Building upon our previous work on security games,[2, 3] we developed a series of game-theoretic models for cyber deception, as well as algorithms to compute the equilibrium or the optimal defender strategy in the games. The first model we proposed is the Cyber Deception Game, a zero-sum Stackelberg game between the defender and an adversary. In this game, the defender is tasked to protect a set of targets, where each target corresponds to a system or a node in a network. Each target has a true configuration, which consists of a set of attributes, e.g., an operating system, services hosted, etc. The defender can choose an observed configuration for each target when responding to probes and scans that may be launched by the attacker. The observed configuration can be different from the true configuration and thus the deception. The attacker, after collecting information about the observed configuration, chooses which target to attack. We show that finding the defender's optimal strategy is NP-hard and provides mixed-integer linear programming (MILP)-based algorithms to compute the optimal deception scheme, and also several heuristic algorithms. In a follow-up work,[7] we extended this game model to a general-sum one, which captures the fact that the cost for the defender may not always be equal to the gain of the attacker. The general-sum nature of this new game model leads to new computational challenges. We provided a Fully Polynomial Time Approximation Scheme (FPTAS) for solving the game and designed a MILP-based algorithm together with several techniques to speed up the computation. In a recent work,[5] we proposed a new attack graph-based Stackelberg security game model and analyze the optimal deception strategy the defender can use. In contrast to previous models, the attacker in this new game can take sequential actions to reach the targets, which is modeled as taking a path on the attack graph. The defender can strategically manipulate the attack graph through deceptive actions in addition to allocating defensive resources to protect important targets from attackers. We provided a MILP-based solution for a special class of attack graphs and a neural architecture search-based method for general directed acyclic attack graphs. We empirically demonstrated the benefit of deception in all these game models and the scalability of the algorithms. This talk features an introduction to these models and algorithms, together with a discussion on future research directions for game theory-based cyber deception.

In the classical problem of scheduling on unrelated parallel machines, a set of jobs has to be assigned to a set of machines. The jobs have a processing time depending on the machine and the goal is to minimize the makespan, that is, the maximum machine load. It is well known that this problem is NP-hard and does not allow polynomial time approximation algorithms with approximation guarantees smaller than 1.5 unless P = NP. We consider the case that there are only a constant number K of machine types. Two machines have the same type if all jobs have the same processing time for them. This variant of the problem is strongly NP-hard already for $$K=1$$ . We present an efficient polynomial time approximation scheme (EPTAS) for the problem, that is, for any $$\varepsilon > 0$$ an assignment with makespan of length at most $$(1+\varepsilon )$$ times the optimum can be found in polynomial time in the input length and the exponent is independent of $$1/\varepsilon $$ . In particular, we achieve a running time of $$2^{{\mathcal {O}}(K\log (K) \nicefrac {1}{\varepsilon }\log ^4 \nicefrac {1}{\varepsilon })}+\mathrm {poly}(|I|)$$ , where |I| denotes the input length. Furthermore, we study three other problem variants and present an EPTAS for each of them: The Santa Claus problem, where the minimum machine load has to be maximized; the case of scheduling on unrelated parallel machines with a constant number of uniform types, where machines of the same type behave like uniformly related machines; and the multidimensional vector scheduling variant of the problem where both the dimension and the number of machine types are constant. For the Santa Claus problem we achieve the same running time. The results are achieved, using mixed integer linear programming and rounding techniques.