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In this paper, we study Resource Constrained Best Upgrade Plan (BUP) computation in road network databases. Consider a transportation network (weighted graph) G where a subset of the edges are upgradable, i.e., for each such edge there is a cost, which if spent, the weight of the edge can be reduced to a specific new value. In the single-pair versi...
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... result of the knapsack algorithm is used as the R temp for pruning. Figure 2 continues the running example of Fig. 1. Assuming a weight of 15 units for every edge whose weight is not explicitly illustrated, and an R temp that achieves a summed path length of 109, Lemma 3 prunes every edge out of the inner (green-border) closed curve. ...
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... of resource ratio In Fig. 12 (single pair) and Fig. 13 (multiple pairs), we vary the resource ratio from 0.2 to 0.8 -that is, B ranges from 20 % to 80 % of C (described in the beginning of the experiment section). A greater ratio implies a larger budget B and, therefore, a smaller SP (s, t, R temp ). In turn, this means more extensive pruning by Lemma 3. Fig. 14, ...
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... Fig. 20 we plot the (percentage of) path length reduction when varying the (original) path length, the upgrade ratio, and the resource ratio, in multiple-pair BUP. The reduc- tion increases with all three parameters. In the first case, that is because as the path length increases, more upgradable edges remain in G c (see Fig. 9) and, ...
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... This problem consists of choosing edges (and nodes) in a network to be upgraded while minimizing costs or satisfying budget constraints [Krumke et al., 1998, Zhang et al., 2004, Baldomero-Naranjo et al., 2022. The problem has seen applications, e.g., in the area of road network optimization, where restricted resources can be used to upgrade edges in order to minimize the travel time between certain source-destination pairs [Lin and Mouratidis, 2015] or where roads can be upgraded to all-weather roads to improve the accessibility of health services [Murawski and Church, 2009]. The BRT investment problem differs from the network improvement problem through being bi-objective and through the consideration of the BRT component constraint. ...
Bus Rapid Transit (BRT) systems can provide a fast and reliable service to passengers at low investment costs compared to tram, metro and train systems. Therefore, they can be of great value to attract more passengers to use public transport. This paper thus focuses on the BRT investment problem: Which segments of a single bus line should be upgraded such that the number of newly attracted passengers is maximized? Motivated by the construction of a new BRT line around Copenhagen, we consider a setting in which multiple parties are responsible for different segments of the line. As each party has a limited willingness to invest, we solve a bi-objective problem to quantify the trade-off between the number of attracted passengers and the investment budget. We model different problem variations: First, we consider two potential passenger responses to upgrades on the line. Second, to prevent scattered upgrades along the line, we consider different restrictions on the number of upgraded connected components on the line. We propose an epsilon-constraint-based algorithm to enumerate the complete set of non-dominated points and investigate the complexity of this problem. Moreover, we perform extensive numerical experiments on artificial instances and a case study based on the BRT line around Copenhagen. Our results show that we can generate the full Pareto front for real-life instances and that the resulting trade-off between investment budget and attracted passengers depends both on the origin-destination demand and on the passenger response to upgrades. Moreover, we illustrate how the generated Pareto plots can assist decision makers in selecting from a set of geographical route alternatives in our case study.
... In network design, the goal is to modify the network so that an objective function modeling a desirable property is optimized. Examples of such objective functions include optimizing shortest path distances (traffic and sustainability improvement) [11,23,27,28], increasing centrality of target nodes by adding a small set of edges [7,18,26], optimizing the -core [24,39], manipulating node similarities [10], and boosting/containing influence on social networks [5,20,25]. ...
In signed networks, each edge is labeled as either positive or negative. The edge sign captures the polarity of a relationship. Balance of signed networks is a well-studied property in graph theory. In a balanced (sub)graph, the vertices can be partitioned into two subsets with negative edges present only across the partitions. Balanced portions of a graph have been shown to increase coherence among its members and lead to better performance. While existing works have focused primarily on finding the largest balanced subgraph inside a graph, we study the network design problem of maximizing balance of a target community (subgraph). In particular, given a budget $b$ and a community of interest within the signed network, we aim to make the community as close to being balanced as possible by deleting up to $b$ edges. Besides establishing NP-hardness, we also show that the problem is non-monotone and non-submodular. To overcome these computational challenges, we propose heuristics based on the spectral relation of balance with the Laplacian spectrum of the network. Since the spectral approach lacks approximation guarantees, we further design a greedy algorithm, and its randomized version, with provable bounds on the approximation quality. The bounds are derived by exploiting pseudo-submodularity of the balance maximization function. Empirical evaluation on eight real-world signed networks establishes that the proposed algorithms are effective, efficient, and scalable to graphs with millions of edges.
... A set of design problems were introduced in [PS95]. Lin et al. [LM15] addressed a shortest path optimization problem via improving edge weights on undirected graphs. The node version of this problem was also studied [DLG11, MVRS18, MBS18]. ...
Covert networks are social networks that often consist of harmful users. Social Network Analysis (SNA) has played an important role in reducing criminal activities (e.g., counter terrorism) via detecting the influential users in such networks. There are various popular measures to quantify how influential or central any vertex is in a network. As expected, strategic and influential miscreants in covert networks would try to hide herself and her partners (called {\em leaders}) from being detected via these measures by introducing new edges. Waniek et al. show that the corresponding computational problem, called Hiding Leader, is NP-Complete for the degree and closeness centrality measures. We study the popular core centrality measure and show that the problem is NP-Complete even when the core centrality of every leader is only $3$. On the contrary, we prove that the problem becomes polynomial time solvable for the degree centrality measure if the degree of every leader is bounded above by any constant. We then focus on the optimization version of the problem and show that the Hiding Leader problem admits a $2$ factor approximation algorithm for the degree centrality measure. We complement it by proving that one cannot hope to have any $(2-\varepsilon)$ factor approximation algorithm for any constant $\varepsilon>0$ unless there is a $\varepsilon/2$ factor polynomial time algorithm for the Densest $k$-Subgraph problem which would be considered a significant breakthrough.
... A set of design problems were introduced in [33]. Lin et al. [26] addressed a shortest path optimization problem via improving edge weights on undirected graphs. Meyerson et al. [28] proposed approximation algorithms for single-source and all-pair shortest paths minimization. ...
Recently, online social networks have become major battlegrounds for political campaigns, viral marketing, and the dissemination of news. As a consequence, ''bad actors'' are increasingly exploiting these platforms, becoming a key challenge for their administrators, businesses and the society in general. The spread of fake news is a classical example of the abuse of social networks by these actors. While some have advocated for stricter policies to control the spread of misinformation in social networks, this often happens in detriment of their democratic and organic structure. In this paper we study how to limit the influence of a target set of users in a network via the removal of a few edges. The idea is to control the diffusion processes while minimizing the amount of disturbance in the network structure. We formulate the influence limitation problem in a data-driven fashion, by taking into account past propagation traces. Moreover, we consider two types of constraints over the set of edge removals, a budget constraint and also a, more general, set of matroid constraints. These problems lead to interesting challenges in terms of algorithm design. For instance, we are able to show that influence limitation is APX-hard and propose deterministic and probabilistic approximation algorithms for the budgeted and matroid version of the problem, respectively. Our experiments show that the proposed solutions outperform the baselines by up to 40%.
... Demaine et al. [17] studied the minimization of the diameter of a network and node eccentricity by adding shortcut edges. Recently, Lin et al. [35] addressed the shortest path distance optimization problem via improving edge weights on undirected graphs. A node version of the problem has also been studied [18,38]. ...
K$-cores are maximal induced subgraphs where all vertices have degree at least $k$. These dense patterns have applications in community detection, network visualization and protein function prediction. However, $k$-cores can be quite unstable to network modifications, which motivates the question: How resilient is the k-core structure of a network, such as the Web or Facebook, to edge deletions? We investigate this question from an algorithmic perspective. More specifically, we study the problem of computing a small set of edges for which the removal minimizes the $k$-core structure of a network. This paper provides a comprehensive characterization of the hardness of the $k$-core minimization problem (KCM), including innaproximability and fixed-parameter intractability. Motivated by such a challenge in terms of algorithm design, we propose a novel algorithm inspired by Shapley value---a cooperative game-theoretic concept--- that is able to leverage the strong interdependencies in the effects of edge removals in the search space. As computing Shapley values is also NP-hard, we efficiently approximate them using a randomized algorithm with probabilistic guarantees. Our experiments, using several real datasets, show that the proposed algorithm outperforms competing solutions in terms of $k$-core minimization while being able to handle large graphs. Moreover, we illustrate how KCM can be applied in the analysis of the $k$-core resilience of networks.
... VLSI, transportation, communication, society), network design provides key controlling capabilities over these systems, especially when resources are constrained. Existing work has investigated the optimization of global network properties, such as minimum spanning tree [12], shortest-path distances [13,7,16], diameter [6], and information diffusion-related metrics [11, 23] via a few ...
... Krumke et al. [12] generalized this model and proposed minimizing the cost of the minimum spanning tree. Lin et al. [13] also proposed a shortest path optimization problem via improving edge weights under a budget constraint. In [7,15], the authors studied the path optimization problem under node improvement. ...
... The importance of this problem has been recognized in the data mining literature [13,17]. The problem is modeled as follows. ...
... The constraints in MIP formulation for POP are shown in Eqs. (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19). The constraints as Eqs. ...
... Later, Krumke et al. [11] generalized this model assuming varying costs for vertex/edge upgrades and proposed algorithms to minimize the cost of the minimum spanning trees. Lin et al. [13] also proposed the shortest path improvement problem where the weights are associated with undirected edges. In all of the above problems, the upgrade models are different and cannot be used to solve out problem. ...
In several domains, the flow of data is governed by an underlying network. Reduction of delays in end-to-end data flow is an important network optimization task. Reduced delays enable shorter travel times for vehicles in road networks, faster information flow in social networks, and increased rate of packets in communication networks. While techniques for network delay minimization have been proposed, they fail to provide any noticeable reduction in individual data flows. Furthermore, they treat all nodes as equally important , which is often not the case in real-world networks. In this paper, we incorporate these practical aspects and propose a network design problem where the goal is to perform k network upgrades such that it maximizes the number of flows in the network with a noticeable reduction in delay. We show that the problem is NP-hard, APX-hard, and non-submodular. We overcome these computational challenges by designing an importance sampling based algorithm with provable quality guarantees. Through extensive experiments on real and synthetic data sets, we establish that importance sampling imparts up to 1000 times speed-up over the greedy approach, and provides up to 70 times the improvement achieved by the state-of-the-art technique.
... VLSI, transportation, communication, society), network design provides key controlling capabilities over these systems, specially when resources are constrained. Existing work has investigated how to optimize global properties, such as minimum spanning tree [16], shortest-path distances [18,8,21], diameter [7], and information diffusion-related metrics [14,30,32] via a few local (e.g. vertex, edge-level) upgrades in the network. ...
... Krumke et al. [16] generalized this model and proposed minimizing the cost of the minimum spanning tree with varying upgrade costs for vertices/edges. Lin et al. [18] also proposed a shortest path optimization problem via improving edge weights under a budget constraint and with undirected edges. In [8,20], the authors studied a different version of the problem, where weights are set to the nodes. ...
Network centrality plays an important role in many applications. Central nodes in social networks can be influential, driving opinions and spreading news or rumors. In hyperlinked environments, such as the Web, where users navigate via clicks, central content receives high traffic, becoming targets for advertising campaigns. While there is an extensive amount of work on centrality measures and their efficient computation, controlling nodes' centrality via network updates is a more recent and challenging problem. Performing minimal modifications to a network to achieve a desired property falls under the umbrella of network design problems. This paper is focused on improving the coverage centrality of a set of nodes, which is the number of shortest paths passing through them, by adding new edges to the network. We prove strong inapproximability results about the problem and propose a greedy algorithm. To ensure applicability to large networks, we design a novel sampling algorithm for centrality optimization with probabilistic approximation guarantees. We further study a constrained yet realistic version of the problem. Besides showing APX-hardness for the restricted problem, we prove our proposed algorithm achieves nearly optimal approximation guarantee.
... Network design problems, including planning, implementing and augmenting networks for desirable properties, have a wide range of applications in communication, transportation and information networks as well as VLSI design [10], [21], [17], [34], [14], [28]. Challenges in this area are posed by the rapidly growing sizes of real-world networks, leading to the need for scalable, data-driven approaches. ...
... Challenges in this area are posed by the rapidly growing sizes of real-world networks, leading to the need for scalable, data-driven approaches. In particular, network design problems involve local changes to an existing large network such as adding/modifying links or nodes as a means to improve its global properties [6], [31], [9], [19], [17], [14]. In this paper we address a problem from the above category, namely, minimizing the overall end-to-end network delay. ...
... the throughput capabilities of individual nodes. The majority of previous work focuses on delay minimization by augmenting network edges [22], [16], [19], [17], [28]. Less attention has been devoted to the complementary, but algorithmically non-equivalent setting in which the propagation capabilities of individual nodes are "upgraded" under budget [9]. ...
Reduction of end-to-end network delays is an optimization task with applications in multiple domains. Low delays enable improved information flow in social networks, quick spread of ideas in collaboration networks, low travel times for vehicles on road networks and increased rate of packets in the case of communication networks. Delay reduction can be achieved by both improving the propagation capabilities of individual nodes and adding additional edges in the network. One of the main challenges in such design problems is that the effects of local changes are not independent, and as a consequence, there is a combinatorial search-space of possible improvements. Thus, minimizing the cumulative propagation delay requires novel scalable and data-driven approaches. In this paper, we consider the problem of network delay minimization via node upgrades. Although the problem is NP-hard, we show that probabilistic approximation for a restricted version can be obtained. We design scalable and high-quality techniques for the general setting based on sampling and targeted to different models of delay distribution. Our methods scale almost linearly with the graph size and consistently outperform competitors in quality.
