The Network Improvement Problem for Equilibrium Routing

In routing games, agents pick their routes through a network to minimize their own delay. A primary concern for the network designer in routing games is the average agent delay at equilibrium. A number of methods to control this average delay have received substantial attention, including network tolls, Stackelberg routing, and edge removal. A related approach with arguably greater practical relevance is that of making investments in improvements to the edges of the network, so that, for a given investment budget, the average delay at equilibrium in the improved network is minimized. This problem has received considerable attention in the literature on transportation research and a number of different algorithms have been studied. To our knowledge, none of this work gives guarantees on the output quality of any polynomial-time algorithm. We study a model for this problem introduced in transportation research literature, and present both hardness results and algorithms that obtain nearly optimal performance guarantees. - We first show that a simple algorithm obtains good approximation guarantees for the problem. Despite its simplicity, we show that for affine delays the approximation ratio of 4/3 obtained by the algorithm cannot be improved. - To obtain better results, we then consider restricted topologies. For graphs consisting of parallel paths with affine delay functions we give an optimal algorithm. However, for graphs that consist of a series of parallel links, we show the problem is weakly NP-hard. - Finally, we consider the problem in series-parallel graphs, and give an FPTAS for this case. Our work thus formalizes the intuition held by transportation researchers that the network improvement problem is hard, and presents topology-dependent algorithms that have provably tight approximation guarantees.Comment: 27 pages (including abstract), 3 figure

Optimized shunting with mixed-usage tracks

We consider the planning of railway freight classification at hump yards, where the problem involves the formation of departing freight train blocks from arriving trains subject to scheduling and capacity constraints. The hump yard layout considered consists of arrival tracks of sufficient length at an arrival yard, a hump, classification tracks of non-uniform and possibly non-sufficient length at a classification yard, and departure tracks of sufficient length. To increase yard capacity, freight cars arriving early can be stored temporarily on specific mixed-usage tracks. The entire hump yard planning process is covered in this paper, and heuristics for arrival and departure track assignment, as well as hump scheduling, have been included to provide the neccessary input data. However, the central problem considered is the classification track allocation problem. This problem has previously been modeled using direct mixed integer programming models, but this approach did not yield lower bounds of sufficient quality to prove optimality. Later attempts focused on a column generation approach based on branch-and-price that could solve problem instances of industrial size. Building upon the column generation approach we introduce a direct arc-based integer programming model, where the arcs are precedence relations between blocks on the same classification track. Further, the most promising models are adapted for rolling-horizon planning. We evaluate the methods on historical data from the Hallsberg shunting yard in Sweden. The results show that the new arc-based model performs as well as the column generation approach. It returns an optimal schedule within the execution time limit for all instances but from one, and executes as fast as the column generation approach. Further, the short execution times of the column generation approach and the arc-indexed model make them suitable for rolling-horizon planning, while the direct mixed integer program proved to be too slow for this. Extended analysis of the results shows that mixing was only required if the maximum number of concurrent trains on the classification yard exceeds 29 (there are 32 available tracks), and that after this point the number of extra car roll-ins increases heavily

Centrality measures and analyzing dot-product graphs

In this thesis we investigate two topics in data mining on graphs; in the first part we investigate the notion of centrality in graphs, in the second part we look at reconstructing graphs from aggregate information. In many graph related problems the goal is to rank nodes based on an importance score. This score is in general referred to as node centrality. In Part I. we start by giving a novel and more efficient algorithm for computing betweenness centrality. In many applications not an individual node but rather a set of nodes is chosen to perform some task. We generalize the notion of centrality to groups of nodes. While group centrality was first formally defined by Everett and Borgatti (1999), we are the first to pose it as a combinatorial optimization problem; find a group of k nodes with largest centrality. We give an algorithm for solving this optimization problem for a general notion of centrality that subsumes various instantiations of centrality that find paths in the graph. We prove that this problem is NP-hard for specific centrality definitions and we provide a universal algorithm for this problem that can be modified to optimize the specific measures. We also investigate the problem of increasing node centrality by adding or deleting edges in the graph. We conclude this part by solving the optimization problem for two specific applications; one for minimizing redundancy in information propagation networks and one for optimizing the expected number of interceptions of a group in a random navigational network. In the second part of the thesis we investigate what we can infer about a bipartite graph if only some aggregate information -- the number of common neighbors among each pair of nodes -- is given. First, we observe that the given data is equivalent to the dot-product of the adjacency vectors of each node. Based on this knowledge we develop an algorithm that is based on SVD-decomposition, that is capable of almost perfectly reconstructing graphs from such neighborhood data. We investigate two versions of this problem, in the versions the dot-product of nodes with themselves, e.g. the node degrees, are either known or hidden

Network improvement for equilibrium routing

Routing games are frequently used to model the behavior of traffic in large networks, such as road networks. In transportation research, the problem of adding capacity to a road network in a cost-effective manner to minimize the total delay at equilibrium is known as the Network Design Problem, and has received considerable attention. However, prior to our work, little was known about guarantees for polynomial-time algorithms for this problem. We obtain tight approximation guarantees for general and series-parallel networks, and present a number of open questions for future work

Simultaneous slack budgeting and retiming for synchronous circuits optimization

Abstract- With the challenges of growing functionality and scaling chip size, the possible performance improvements should be considered in the earlier IC design stages, which gives more freedom to the later optimization. Potential slack as an effective metric of possible performance improvements is considered in this work which, as far as we known, is the first work that maximizes the potential slack by retiming for synchronous sequential circuit. A simultaneous slack budgeting and incremental retiming algorithm is proposed for maximizing potential slack. The overall slack budget is optimized by relocating the FFs iteratively with the MIS-based slack estimation. Compared with the potential slack of a well-known min-period retiming, our algorithm improves potential slack averagely 19.6 % without degrading the circuit performance in reasonable runtime. Furthermore, at the expense of a small amount of timing performance, 0.52 % and 2.08%, the potential slack is increased averagely by 19.89 % and 28.16 % separately, which give a hint of the tradeoff between the timing performance and the slack budget.

Robust optimization models for the dicrete time/cost trade-off problem

Cataloged from PDF version of article.Developing models and algorithms to generate robust project schedules that are less sensitive to disturbances are essential in today’s highly competitive uncertain project environments. This paper addresses robust scheduling in project environments; specifically, we address the discrete time/cost trade-off problem (DTCTP). We formulate the robust DTCTP with three alternative optimization models in which interval uncertainty is assumed for the unknown cost parameters. We develop exact and heuristic algorithms to solve these robust optimization models. Furthermore, we compare the schedules that have been generated with these models on the basis of schedule robustness. & 2010 Elsevier B.V. All rights reserved