We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.

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CasADi: a software framework for nonlinear optimization and optimal control

Matching is a classic problem with a rich history and a significant impact, both on the theory of algorithms and in practice. Recently there has been a surge of interest in the online version of matching and its generalizations, due to the important new application domain of Internet advertising. The theory of online matching and allocation has played a critical role in designing algorithms for ad allocation. This monograph surveys the key problems, models and algorithms from online matchings, as well as their implication in the practice of ad allocation. The goal is to provide a classification of the problems in this area, an introduction into the techniques used, a glimpse into the practical impact, and to provide direction in terms of open questions. Matching continues to find core applications in diverse domains, and the advent of massive online and streaming data emphasizes the future applicability of the algorithms and techniques surveyed here.

/pdf/online-matching-and-ad-allocation-2bagnfnhyu.pdf

Online Matching and Ad Allocation

With the rapid development of smartphones, spatial crowdsourcing platforms are getting popular. A foundational research of spatial crowdsourcing is to allocate micro-tasks to suitable crowd workers. Most existing studies focus on offline scenarios, where all the spatiotemporal information of micro-tasks and crowd workers is given. However, they are impractical since micro-tasks and crowd workers in real applications appear dynamically and their spatiotemporal information cannot be known in advance. In this paper, to address the shortcomings of existing offline approaches, we first identify a more practical micro-task allocation problem, called the Global Online Micro-task Allocation in spatial crowdsourcing (GOMA) problem. We first extend the state-of-art algorithm for the online maximum weighted bipartite matching problem to the GOMA problem as the baseline algorithm. Although the baseline algorithm provides theoretical guarantee for the worst case, its average performance in practice is not good enough since the worst case happens with a very low probability in real world. Thus, we consider the average performance of online algorithms, a.k.a online random order model.We propose a two-phase-based framework, based on which we present the TGOA algorithm with 1 over 4 -competitive ratio under the online random order model. To improve its efficiency, we further design the TGOA-Greedy algorithm following the framework, which runs faster than the TGOA algorithm but has lower competitive ratio of 1 over 8. Finally, we verify the effectiveness and efficiency of the proposed methods through extensive experiments on real and synthetic datasets.

/pdf/online-mobile-micro-task-allocation-in-spatial-crowdsourcing-16opveojqm.pdf

Online mobile Micro-Task Allocation in spatial crowdsourcing

Crowdsourcing is a computing paradigm where humans are actively involved in a computing task, especially for tasks that are intrinsically easier for humans than for computers. Spatial crowdsourcing is an increasing popular category of crowdsourcing in the era of mobile Internet and sharing economy, where tasks are spatiotemporal and must be completed at a specific location and time. In fact, spatial crowdsourcing has stimulated a series of recent industrial successes including sharing economy for urban services (Uber and Gigwalk) and spatiotemporal data collection (OpenStreetMap and Waze). This survey dives deep into the challenges and techniques brought by the unique characteristics of spatial crowdsourcing. Particularly, we identify four core algorithmic issues in spatial crowdsourcing: (1) task assignment, (2) quality control, (3) incentive mechanism design, and (4) privacy protection. We conduct a comprehensive and systematic review of existing research on the aforementioned four issues. We also analyze representative spatial crowdsourcing applications and explain how they are enabled by these four technical issues. Finally, we discuss open questions that need to be addressed for future spatial crowdsourcing research and applications.

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=5938&context=sis_research

Spatial crowdsourcing: a survey

Modern global routers employ various routing methods to improve routing speed and quality Maze routing is the most time-consuming process for existing global routing algorithms This paper presents two bounded-length maze routing (BLMR) algorithms (optimal-BLMR and heuristic-BLMR) that perform much faster routing than traditional maze routing algorithms In addition, a rectilinear Steiner minimum tree aware routing scheme is proposed to guide heuristic-BLMR and monotonic routing to build a routing tree with shorter wirelength This paper also proposes a parallel multithreaded collision-aware global router based on a previous sequential global router (SGR) Unlike the partitioning-based strategy, the proposed parallel router uses a task-based concurrency strategy Finally, a 3-D wirelength optimization technique is proposed to further refine the 3-D routing results Experimental results reveal that the proposed SGR uses less wirelength and runs faster than most of other state-of-the-art global routers with a different set of parameters , , ,  Compared to the proposed SGR, the proposed parallel router yields almost the same routing quality with average 271 and 312-fold speedup on overflow-free and hard-to-route cases, respectively, when running on a 4-core system

https://ir.nctu.edu.tw:443/bitstream/11536/21646/1/000318163800005.pdf

NCTU-GR 2.0: Multithreaded Collision-Aware Global Routing With Bounded-Length Maze Routing

We study online variants of weighted bipartite matching on graphs and hypergraphs. In our model for online matching, the vertices on the right-hand side of a bipartite graph are given in advance and the vertices on the left-hand side arrive online in random order. Whenever a vertex arrives, its adjacent edges with the corresponding weights are revealed and the online algorithm has to decide which of these edges should be included in the matching. The studied matching problems have applications, e.g., in online ad auctions and combinatorial auctions where the right-hand side vertices correspond to items and the left-hand side vertices to bidders.

An Optimal Online Algorithm for Weighted Bipartite Matching and Extensions to Combinatorial Auctions

We study packing LPs in an online model where the columns are presented to the algorithm in random order. This natural problem was investigated in various recent studies motivated, e.g., by online ad allocations and yield management where rows correspond to resources and columns to requests specifying demands for resources. Our main contribution is a $1-O(\sqrt{(\log{d})/B})$-competitive online algorithm, where $d$ denotes the column sparsity, i.e., the maximum number of resources that occur in a single column, and $B$ denotes the capacity ratio $B$, i.e., the ratio between the capacity of a resource and the maximum demand for this resource. In other words, we achieve a $(1 - \epsilon)$-approximation if the capacity ratio satisfies $B=\Omega((\log d)/\epsilon^2)$, which is known to be best-possible for any (randomized) online algorithms. 
Our result improves exponentially on previous work with respect to the capacity ratio. In contrast to existing results on packing LP problems, our algorithm does not use dual prices to guide the allocation of resources. Instead, it simply solves, for each request, a scaled version of the partially known primal program and randomly rounds the obtained fractional solution to obtain an integral allocation for this request. We show that this simple algorithmic technique is not restricted to packing LPs with large capacity ratio: We prove an upper bound on the competitive ratio of $\Omega(d^{-1/(B-1)})$, for any $B \ge 2$. In addition, we show that our approach can be combined with VCG payments and obtain an incentive compatible $(1-\epsilon)$-competitive mechanism for packing LPs with $B=\Omega((\log m)/\epsilon^2)$, where $m$ is the number of constraints. Finally, we apply our technique to the generalized assignment problem for which we obtain the first online algorithm with competitive ratio $O(1)$.

Primal Beats Dual on Online Packing LPs in the Random-Order Model

We study packing LPs in an online model where the columns are presented to the algorithm in random order. This natural problem was investigated in various recent studies motivated, e.g., by online ad allocations and yield management where rows correspond to resources and columns to requests specifying demands for resources. Our main contribution is a 1 -- O(√(log d/B))-competitive online algorithm. Here d denotes the column sparsity, i.e., the maximum number of resources that occur in a single column, and B denotes the capacity ratio B, i.e., the ratio between the capacity of a resource and the maximum demand for this resource. In other words, we achieve a (1--e)-approximation if the capacity ratio satisfies B=Ω(logd/e2), which is known to be best-possible for any (randomized) online algorithms. Our result improves exponentially on previous work with respect to the capacity ratio. In contrast to existing results on packing LP problems, our algorithm does not use dual prices to guide the allocation of resources over time. Instead, the algorithm simply solves, for each request, a scaled version of the partially known primal program and randomly rounds the obtained fractional solution to obtain an integral allocation for this request. We show that this simple algorithmic technique is not restricted to packing LPs with large capacity ratio of order Ω(logd), but it also yields close-to-optimal competitive ratios if the capacity ratio is bounded by a constant. In particular, we prove an upper bound on the competitive ratio of Ω(d--1/(B--1)), for any B ≥ 2. In addition, we show that our approach can be combined with VCG payments and obtain an incentive compatible (1 -- e)-competitive mechanism for packing LPs with B = Ω(logm/e;2), where m is the number of constraints. Finally, we apply our technique to the generalized assignment problem for which we obtain the first online algorithm with competitive ratio O(1).

Primal beats dual on online packing LPs in the random-order model

We consider the (block-angular) min–max resource sharing problem, which is defined as follows. Given finite sets $${\mathcal{R}}$$
 of resources and $${\mathcal{C}}$$
 of customers, a convex set $${\mathcal{B}_c}$$
 , called block, and a convex function $${g_c:\mathcal{B}_c\to\mathbb{R}_{+}^{\mathcal{R}}}$$
 for every $${c\in\mathcal{C}}$$
 , the task is to find $${b_c\in\mathcal{B}_c\ (c\in\mathcal{C})}$$
 approximately attaining $${\lambda^*:=\inf\{\max_{r\in\mathcal{R}}\sum_{c\in\mathcal{C}}(g_c(b_c))_r \mid b_c\in\mathcal{B}_c\ (c\in\mathcal{C})\}}$$
 . As usual we assume that g
 c
 can be computed efficiently and we have a constant σ ≥ 1 and oracle functions $${f_c : \mathbb{R}_{+}^{\mathcal{R}} \rightarrow \mathcal{B}_c}$$
 , called block solvers, which for $${c \in \mathcal{C}}$$
 and $${y \in \mathbb{R}_{+}^{\mathcal{R}}}$$
 return an element $${b_c \in \mathcal{B}_c}$$
 with $${y^{\scriptscriptstyle\top}{g_c(b_c)} \leq \sigma \inf_{b \in \mathcal{B}_c} y^{\scriptscriptstyle\top}{g_c(b)}}$$
 . We describe a simple algorithm which solves this problem with an approximation guarantee σ(1 + ω) for any ω > 0, and whose running time is $${O(\theta(|\mathcal{C}|+|\mathcal{R}|) \log|\mathcal{R}|(\log\log|\mathcal{R}|+\omega^{-2}))}$$
 for any fixed σ ≥ 1, where θ is the time for an oracle call. This generalizes and improves various previous results. We also prove other bounds and describe several speed-up techniques. In particular, we show how to parallelize the algorithm efficiently. In addition we review another algorithm, variants of which were studied before. We show that this algorithm is almost as fast in theory, but it was not competitive in our experiments. Our work was motivated mainly by global routing in chip design. Here the blocks are mixed-integer sets (whose elements are associated with Steiner trees), and we combine our algorithm with randomized rounding. We present experimental results on instances resulting from recent industrial chips, with millions of customers and resources. Our algorithm solves these instances nearly optimally in less than two hours.

Faster min–max resource sharing in theory and practice

We study packing linear programs (LPs) in an online model where the columns are presented to the algorithm in random order. This natural problem was investigated in various recent studies motivated...

Klaus Radke

Papers

An Optimal Online Algorithm for Weighted Bipartite Matching and Extensions to Combinatorial Auctions

Primal Beats Dual on Online Packing LPs in the Random-Order Model

Primal beats dual on online packing LPs in the random-order model

Faster min–max resource sharing in theory and practice

Primal Beats Dual on Online Packing LPs in the Random-Order Model