Guaranteed Approximation Ratio Research Articles

Practical Algorithms with Guaranteed Approximation Ratio for Traveling Tournament Problem with Maximum Tour Length 2

The traveling tournament problem (TTP) is a hard but interesting sports scheduling problem inspired by Major League Baseball, which is to design a double round-robin schedule such that each pair of teams plays one game in each other’s home venue, minimizing the total distance traveled by all n teams (n is even). In this paper, we consider TTP-2 (i.e., TTP under the constraint that at most two consecutive home games or away games are allowed for each team). In this paper, we propose practical algorithms for TTP-2 with improved approximation ratios. Because of the different structural properties of the problem, all known algorithms for TTP-2 are different for n/2 being odd and even, and our algorithms are also different for these two cases. For even n/2, our approximation ratio is [Formula: see text], improving the previous result of [Formula: see text]. For odd n/2, our approximation ratio is [Formula: see text], improving the previous result of [Formula: see text]. In practice, our algorithms are easy to implement. Experiments on well-known benchmark sets show that our algorithms beat previously known solutions for all instances with an average improvement of 5.66%. Funding: This work was supported by the National Natural Science Foundation of China [Grants 62372095 and 62172077] and the Sichuan Natural Science Foundation [Grant 2023NSFSC0059].

Evolutionary Algorithm on General Cover with Theoretically Guaranteed Approximation Ratio

Theoretical studies on evolutionary algorithms have developed vigorously in recent years. Many such algorithms have theoretical guarantees in both running time and approximation ratio. Some approximation mechanism seems to be inherently embedded in many evolutionary algorithms. In this paper, we identify such a relation by proposing a unified analysis framework for a global simple multiobjective evolutionary algorithm (GSEMO) and apply it on a minimum weight general cover problem, which is general enough to subsume many important problems including the minimum submodular cover problem in which the submodular function is real-valued, and the minimum connected dominating set problem for which the potential function is nonsubmodular. We show that GSEMO yields theoretically guaranteed approximation ratios matching those achievable by a greedy algorithm in expected polynomial time when the potential function g is polynomial in the input size and the minimum gap between different g-values is a constant. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This work was supported by National Natural Science Foundation of China [11771013, U20A2068]; Zhejiang Provincial Natural Science Foundation of China [LD19A010001].

Approximating Minimum k-Tree Cover of a Connected Graph Inspired by the Multi-Ferry Routing in Delay Tolerant Networks

In this paper, we consider the problem of covering the vertex set of a given graph by [Formula: see text] trees so as to minimize the maximum weight of the trees, as a subproblem of the multi-ferry scheduling problem proposed by Zhao and Ammar. After pointing out that the approximation ratio of a greedy scheme based on the Kruskal’s algorithm is provably bad, we show that the approximation ratio cannot be better than 3/2 for [Formula: see text] even when the edge selection criterion is modified so as to minimize the increase in the maximum weight in the collection of trees. We then propose two polynomial-time algorithms with a guaranteed approximation ratio. The first algorithm achieves 3-approximation for the class of graphs in which the edge weights satisfy the triangle inequality. The second algorithm achieves 4-approximation for any connected graph with arbitrary edge weights.

TED: Towards Discovering Top-k Edge-Diversified Patterns in a Graph Database

With an exponentially growing number of graphs from disparate repositories, there is a strong need to analyze a graph database containing an extensive collection of small- or medium-sized data graphs (e.g., chemical compounds). Although subgraph enumeration and subgraph mining have been proposed to bring insights into a graph database by a set of subgraph structures, they often end up with similar or homogenous topologies, which is undesirable in many graph applications. To address this limitation, we propose the Top-k Edge-Diversified Patterns Discovery problem to retrieve a set of subgraphs that cover the maximum number of edges in a database. To efficiently process such query, we present a generic and extensible framework called Ted which achieves a guaranteed approximation ratio to the optimal result. Two optimization strategies are further developed to improve the performance. Experimental studies on real-world datasets demonstrate the superiority of Ted to traditional techniques.

Optimizing Cross-Line Dispatching for Minimum Electric Bus Fleet

Recent years have witnessed the increasing popularity of electric buses (e-buses) around the globe due to their environment friendly nature. However, various factors, such as the prohibitive purchasing costs and the scarcity of large-scale charging facilities, hinder the wider adoption of e-buses. Thus, to effectively cut the cost of building and maintaining urban e-bus systems, we optimize the dispatching strategy for urban e-bus systems to satisfy public transportation demands with the minimum e-bus fleet. Specifically, we propose to systematically exploit at city-scale cross-line dispatching, a smart dispatching strategy allowing one bus to serve multiple bus lines when necessary. Technically, we construct a novel and generalizable graph-theoretic model for urban e-bus systems integrating e-buses non-negligible charging time, the spatio-temporal constraints of bus trips, and various other real-world factors. We prove that it is NP-hard, and has no <inline-formula><tex-math notation="LaTeX">$(2-\epsilon)$</tex-math></inline-formula> -approximation algorithm. Next, we propose a polynomial-time algorithm solving the problem with a guaranteed approximation ratio. Furthermore, we conduct extensive experiments on a large-scale real-world bus dataset from Shenzhen, China, which validate the effectiveness of our algorithms. As shown by our experimental results, to serve 300 bus lines, our dispatching strategy needs 38.2% less e-buses than the one currently used in practice.

Exact and approximate determination of the Pareto front using Minimal Correction Subsets

Recently, it has been shown that the enumeration of Minimal Correction Subsets (MCS) of Boolean formulas allows solving Multi-Objective Boolean Optimization (MOBO) formulations. However, a major drawback of this approach is that most MCSs do not correspond to Pareto-optimal solutions. In fact, one can only know that a given MCS corresponds to a Pareto-optimal solution when all MCSs are enumerated. Moreover, if it is not possible to enumerate all MCSs, then there is no guarantee of the quality of the approximation of the Pareto frontier. This paper extends the state of the art for solving MOBO using MCSs. First, we show that it is possible to use MCS enumeration to solve MOBO problems such that each MCS necessarily corresponds to a Pareto-optimal solution. Additionally, we also propose two new algorithms that can find a (1+ɛ)-approximation of the Pareto frontier using MCS enumeration. Experimental results in several benchmark sets show that the newly proposed algorithms allow finding better approximations of the Pareto frontier than state-of-the-art algorithms, and with guaranteed approximation ratios.

Optimizing the Age of Information for Multi-Source Information Update in Internet of Things

Age of Information (AoI) has recently become a new performance metric that captures the freshness/timeliness of information at end users in Internet of Things (IoT). Most existing information update mechanisms mainly consider the status information from a single Source Node (SN) or from multiple SNs with independent observations. However, in a practical IoT system, each status could be observed by multiple SNs, which brings new challenge in optimizing the AoI. To consider this issue, this paper formulates two optimization problems, named AoI-aware Multi-source Information Update problem (<i>AoI-MSIU</i>) and AoI-Reduction-aware Multi-source Information Update problem (<i>AoIR-MSIU</i>) problem, respectively. Specifically, AoI-MSIU problem assumes that the status are the first time to be uploaded to the BS, while AoIR-MSIU problem supposes that the BS already maintains the status that it has received before. Besides maximizing the revenue of information update, both problems consider how to optimize the AoI of the status. For AoI-MSIU problem, we prove that it is NP-hard, and propose an efficient greedy algorithm with a guaranteed approximation ratio. For AoIR-MSIU problem, we propose a polynomial-time optimal solution, which is based on a maximum weight bipartite matching on an auxiliary graph. Finally, we evaluate the performance of the proposed schemes through simulations.

Significant Geo-Social Group Discovery over Location-Based Social Network

Geo-social community detection over location-based social networks combining both location and social factors to generate useful computational results has attracted increasing interest from both industrial and academic communities. In this paper, we formulate a novel community model, termed geo-social group (GSG), to enforce both spatial and social factors to generate significant computational patterns and to investigate the problem of community detection over location-based social networks. Specifically, GSG detection aims to extract all group-venue clusters, where users are similar to each other in the same group and they are located in a minimum covering circle (MCC) for which the radius is no greater than a distance threshold . Then, we present a GSGD algorithm following a three-step paradigm to enumerate all qualified GSGs in a large network. We propose effective optimization techniques to efficiently enumerate all communities in a network. Furthermore, we extend a significant GSG detection problem to top-k geo-social group (TkGSG) mining. Rather than extracting all qualified GSGs in a network, TkGSG aims to return k feasibility groups to guarantee the diversity. We prove the hardness of computing the TkGSGs. Nevertheless, we propose the effective greedy approach with a guaranteed approximation ratio of . Extensive empirical studies on real and synthetic networks show the superiority of our algorithm when compared with existing methods and demonstrate the effectiveness of our new community model and the efficiency of our optimization techniques.

Access Strategies for Network Caching

Having multiple data stores that can potentially serve content is common in modern networked applications. Data stores often publish approximate summaries of their content to enable effective utilization. Since these summaries are not entirely accurate, forming an efficient access strategy to multiple data stores becomes a complex risk management problem. This paper formally models this problem as a cost minimization problem, while taking into account both access costs, the inaccuracy of the approximate summaries, as well as the penalties incurred by failed requests. We introduce practical algorithms with guaranteed approximation ratios and further show that they are optimal in various settings. We also perform an extensive simulation study based on real data and show that our algorithms are more robust than existing heuristics. That is, they exhibit near-optimal performance in various settings, whereas the efficiency of existing approaches depends upon system parameters that may change over time, or be otherwise unknown.

Joint Index Coding and Incentive Design for Selfish Clients

The index coding problem includes a server, a group of clients, and a set of data chunks. While each client wants a subset of the data chunks and already has another subset as its side information, the server transmits some (uncoded or coded) chunks to the clients over a noiseless broadcast channel. The objective of the problem is to satisfy the demands of all clients with the minimum number of transmissions. This paper investigates the index coding setting from a game-theoretical perspective. We consider selfish clients, where each selfish client has private side information and a private valuation of each data chunk it wants. In this context, our objectives are following: 1) to motivate each selfish client to reveal the correct side information and true valuation of each data chunk it wants; 2) to maximize the social welfare, i.e., the total valuation of the data chunks recovered by the clients minus the total cost incurred by the transmissions from the server. Our main contribution is to jointly develop coding and incentive schemes for achieving the first objective perfectly and achieving the second objective optimally or approximately with guaranteed approximation ratios (potentially within some restricted sets of coding matrices).

Efficient Radius-Bounded Community Search in Geo-Social Networks

Driven by real-life applications in geo-social networks, we study the problem of computing radius-bounded <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -cores (RB- <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -cores) that aims to find communities satisfying both social and spatial constraints. In particular, the model <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -core (i.e., the subgraph where each vertex has at least <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> neighbors) is used to ensure the social cohesiveness, and a radius-bounded circle is used to restrict the locations of users in an RB- <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -core. We explore several algorithmic paradigms to compute RB- <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -cores, including a triple-vertex-based paradigm, a binary-vertex-based paradigm, and a paradigm utilizing the concept of rotating circles. The rotating-circle-based paradigm is further enhanced by several pruning techniques to achieve better efficiency. In addition, to find representative RB- <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -cores, we study the diversified radius-bounded <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -core search problem, which finds <inline-formula><tex-math notation="LaTeX">$t$</tex-math></inline-formula> RB- <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -cores to cover the most number of vertices. We first propose a baseline algorithm that identifies the distinctive RB- <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -cores after finding all the RB- <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -cores. Beyond this, we design algorithms that can efficiently maintain the top- <inline-formula><tex-math notation="LaTeX">$t$</tex-math></inline-formula> candidate RB- <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -cores and also achieve a guaranteed approximation ratio. Experimental studies on both real and synthetic datasets demonstrate that our proposed techniques can efficiently compute (diversified) RB- <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -cores. Moreover, our techniques can be used to compute the minimum-circle-bounded <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -core and significantly outperform the existing techniques.

Incentive-Aware Recruitment of Intelligent Vehicles for Edge-Assisted Mobile Crowdsensing

Edge-assisted mobile crowdsensing is an emerging paradigm where mobile users collect, and share sensing data at the edge of networks. With the abundant on-board resources, and large movement patterns of intelligent vehicles, they have become candidates to sense up-to-date, and fine-grained information for large areas. The design of vehicle recruitment in edge-assisted mobile crowdsensing is challenging due to the selfishness, and the uneven distribution of vehicles, as well as the spatiotemporal constraints of vehicular crowdsensing applications. To deal with these challenges, this paper proposes an incentive-aware vehicle recruitment scheme for edge-assisted mobile crowdsensing. In particular, we first design an incentive mechanism to motivate cooperation among the edge server, and the intelligent vehicles, and apply the Nash bargaining theory to obtain the optimal cooperation decision. Furthermore, a practical, and efficient scheme is proposed to weigh the contribution of vehicles. Then, we formulate the participant recruitment as an optimization problem, and prove that it is NP-hard. To address this problem, an effective heuristic algorithm with a guaranteed approximation ratio is proposed, by leveraging the property in submodular optimization. Finally, we conduct extensive simulations, based on a real dataset, to validate the superiority of the proposed schemes.

A Polynomial Algorithm with Asymptotic Ratio $$\boldsymbol {2/3}$$ for the Asymmetric Maximization Version of the $$\boldsymbol m $$-PSP

In 2005, Kaplan et al. presented a polynomial-time algorithm with guaranteed approximation ratio $$2/3$$ for the maximization version of the asymmetric TSP. In 2014, Glebov, Skretneva, and Zambalaeva constructed a similar algorithm with approximation ratio $$2/3 $$ and cubic runtime for the maximization version of the asymmetric $$2 $$ -PSP ( $$2 $$ -APSP-max), where it is required to find two edge-disjoint Hamiltonian cycles of maximum total weight in a complete directed weighted graph. The goal of this paper is to construct a similar algorithm for the more general $$m $$ -APSP-max in the asymmetric case and justify an approximation ratio for this algorithm that tends to $$2/3 $$ as $$n$$ grows and the runtime complexity estimate $$O(mn^3)$$ .

Minimum Cost Feedback Selection in Structured Systems: Hardness and Approximation Algorithm

This article deals with output feedback selection in linear time-invariant structured systems. We assume that the inputs and the outputs are dedicated , i.e., each input directly actuates a single state and each output directly senses a single state. Given a structured system with dedicated inputs and outputs and a cost matrix that denotes the cost of each feedback connection, our aim is to select a minimum cost set of feedback connections such that the closed-loop system satisfies arbitrary pole-placement. This problem is referred to as the optimal feedback selection problem for dedicated i/o. The optimal feedback selection problem for dedicated i/o is NP-hard and inapproximable to a constant factor of log $ n$ , where $n$ denotes the system dimension. To this end, we propose an algorithm to find an approximate solution to the problem. The proposed algorithm consists of a potential function incorporated with a greedy scheme and attains a solution with a guaranteed approximation ratio. We consider two special network topologies of practical importance, referred to as back-edge feedback structure and hierarchical networks . For the first case, which is NP-hard and inapproximable to a multiplicative factor of log $ n$ , we provide a $\text{log} n$ -approximate solution. For hierarchical networks, we give a dynamic programming based algorithm to obtain an optimal solution in polynomial time.

Group sweep coverage with guaranteed approximation ratio

Wireless Sensor Networks (WSNs) are often deployed to monitor a region of interest. With sweep coverage, mobile sensor nodes are scheduled to move along a planned route (i.e. sweep route) in order to collect the data from a series of Point of Interests (POIs) sequentially. In this paper, we generalize the sweep coverage problem by proposing a new coverage paradigm, group sweep coverage. With group sweep coverage, the POIs are divided into several groups. A group is said to be covered when one of the POIs in the group is covered. The goal in group sweep coverage is to construct a sweep route that mobile sensor nodes should follow in order to cover all groups during each predefined period. In our research, we devised two algorithms for group sweep coverage: AGSC and DSRM. AGSC is a centralized scheme whose approximation ratio is 5Δ. Namely, the length of the sweep route generated by AGSC is at most 5Δ times that of the optimal sweep route. DSRM is a distributed scheme for large-scale networks with dynamic POIs. Compared with AGSC, DSRM leads to the same approximation ratio and better scalability. Our experimental results indicate that both AGSC and DSRM outperform the state-of-the-art schemes in terms of average and maximal sweep route length.

Efficient community discovery with user engagement and similarity

In this paper, we investigate the problem of (k,r)-core which intends to find cohesive subgraphs on social networks considering both user engagement and similarity perspectives. In particular, we adopt the popular concept of k-core to guarantee the engagement of the users (vertices) in a group (subgraph) where each vertex in a (k,r)-core connects to at least k other vertices. Meanwhile, we consider the pairwise similarity among users based on their attributes. Efficient algorithms are proposed to enumerate all maximal (k,r)-cores and find the maximum (k,r)-core, where both problems are shown to be NP-hard. Effective pruning techniques substantially reduce the search space of two algorithms. A novel ($$k$$,$$k'$$)-core based ($$k$$,$$r$$)-core size upper bound enhances the performance of the maximum (k,r)-core computation. We also devise effective search orders for two algorithms with different search priorities for vertices. Besides, we study the diversified ($$k$$,$$r$$)-core search problem to find l maximal ($$k$$,$$r$$)-cores which cover the most vertices in total. These maximal ($$k$$,$$r$$)-cores are distinctive and informationally rich. An efficient algorithm is proposed with a guaranteed approximation ratio. We design a tight upper bound to prune unpromising partial ($$k$$,$$r$$)-cores. A new search order is designed to speed up the search. Initial candidates with large size are generated to further enhance the pruning power. Comprehensive experiments on real-life data demonstrate that the maximal (k,r)-cores enable us to find interesting cohesive subgraphs, and performance of three mining algorithms is effectively improved by all the proposed techniques.

Cost-Efficient Scheduling of Bulk Transfers in Inter-Datacenter WANs

With the quick growth of traffic between data centers, inefficient transfer scheduling in inter-datacenter networks can lead to a huge waste of bandwidth thus significant bandwidth cost. Previous work have explored different ways, such as software-defined WANs and dynamic pricing mechanisms, to overcome the inefficiency of inter-datacenter networks. However, there is a big challenge in addressing the fundamental conflicts between the deadline-aware transfer scheduling and minimizing the bandwidth cost. Unlike existing efforts that schedule inter-datacenter transfers under fixed link capacities, wherein some deadlines are violated and the service quality is degraded, we aim to finish all the transfers on time with as little bandwidth as possible to minimize the bandwidth cost. We take into account the variation of bandwidth price and the deadline requirements of services, and formulate the problem of cost-efficient scheduling of bulk transfers with deadline guarantee, which is shown to be NP-hard. Benefitting from the relax-and-round method, we propose a progressively-descending algorithm (PDA) to schedule bulk transfers and meet the above goals with a guaranteed approximation ratio. We apply our algorithm in a bulk transfer scheduler, Butler, and build a small-scale testbed to evaluate its efficiency. Both large-scale simulation and testbed experiment results validate the ability of our scheme on cutting down the bandwidth cost. Compared with existing approaches, it reduces up to 60% bandwidth cost and increases the network utilization by up to 140%.

Data mule scheduling on a path with handling time and time span constraints

In this paper, we study a data mule scheduling problem in which data mules are dispatched from a depot to serve targets located on a path. Every target sensor has a handling time, and every data mule is required to return to the depot before time span D. The goal is to minimize the number of data mules. For uniform handling time, a linear-time algorithm is presented. For non-uniform handling time, NP-hardness is proved and an approximation algorithm with a guaranteed approximation ratio is presented.

Thanos: Incentive Mechanism with Quality Awareness for Mobile Crowd Sensing

Recent years have witnessed the emergence of mobile crowd sensing (MCS) systems, which leverage the public crowd equipped with various mobile devices for large scale sensing tasks. In this paper, we study a critical problem in MCS systems, namely, incentivizing worker participation. Different from existing work, we propose an incentive framework for MCS systems, named Thanos, that incorporates a crucial metric, called workers’ quality of information (QoI). Due to various factors (e.g., sensor quality and environment noise), the quality of the sensory data contributed by individual workers varies significantly. Obtaining high quality data with little expense is always the ideal of MCS platforms. Technically, our design of Thanos is based on reverse combinatorial auctions. We investigate both the single- and multi-minded combinatorial auction models. For the former, we design a truthful, individual rational, and computationally efficient mechanism that ensures a close-to-optimal social welfare. For the latter, we design an iterative descending mechanism that satisfies individual rationality and computational efficiency, and approximately maximizes the social welfare with a guaranteed approximation ratio. Through extensive simulations, we validate our theoretical analysis on the various desirable properties guaranteed by Thanos.

Minimizing machine assignment costs over Δ-approximate solutions of the scheduling problem P||Cmax

Bi-criteria lexicographical minimization problems with the makespan as the primary objective and the total machine assignment costs as the secondary objective have been recently introduced to the scheduling research, and polynomial time (r+1,1)-approximation algorithms have been suggested for their solution, where 1<r<2 is the performance ratio of an approximation algorithm for P||Cmax. We improve these results by presenting a polynomial time (1.5r−1,1)-approximation algorithm for the additive cost type. Then, we introduce a problem of minimizing the total machine assignment cost over the Δ-approximate solutions of the makespan minimization problem. We prove that this new problem is strongly NP-hard and pseudo-polynomially non-approximable in general. A polynomial time approximation algorithm with a guaranteed approximation ratio is presented for the additive cost type and bounded ratio between the maximal and minimal machine costs. An O(mn2k) time dynamic programming algorithm is also presented, where k is the fixed number of distinct job processing times.