Ching-Lueh Chang, Yuh-Dauh Lyuu
We parallelize several previously proposed algorithms for the minimum routing cost spanning tree problem and some related problems.
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We study the problem of computing all Pareto-optimal journeys in a public transit network regarding the two criteria of arrival time and number of transfers taken. In recent years, great advances have been made in making public transit network routing more scalable to larger networks. However, most approaches are silent on scalability in another dimension: Time. Experimental evaluations are often done on slices of timetables spanning a couple of days, when in reality, the planning horizon is much longer. We introduce an extension to trip-based public transit routing, proposed in [12], that all…
Light Tree Covers, Routing, and Path-Reporting Oracles via Spanning Tree Covers in Doubling Graphs
本文通过构造倍增图的(1+ε)-拉伸生成树覆盖，解决了树覆盖恒定轻度这一长期开放问题，并由此得到轻量树覆盖、紧凑路由方案和路径报告距离预言机等应用。
We study the strategic decision-making problem of assigning time windows to customers in the context of vehicle routing applications that are affected by operational uncertainty. This problem, known as the Time Window Assignment Vehicle Routing Problem, can be viewed as a two-stage stochastic optimization problem, where time window assignments constitute first-stage decisions, vehicle routes adhering to the assigned time windows constitute second-stage decisions, and the objective is to minimize the expected routing costs. We prove that a sampled deterministic equivalent of this stochastic mod…
A weakness of next-hop routing is that following a link or router failure there may be no routes between some source-destination pairs, or packets may get stuck in a routing loop as the protocol operates to establish new routes. In this article, we address these weaknesses by describing mechanisms to choose alternate next hops. Our first contribution is to model the scenario as the following {\sc tree augmentation} problem. Consider a mixed graph where some edges are directed and some undirected. The directed edges form a spanning tree pointing towards the common destination node. Each directe…
We study the NP-hard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph $G$ over $n$ nodes that minimizes the sum of distances between all pairs of nodes. In the considered model every node can transmit a different (but short) message to each of its neighbors in each synchronous round. We provide a randomized $(2+ε)$-approximation with runtime $O(D+\frac{\log n}ε)$ for unweighted graphs. Here, $D$ is the diameter of $G$. This improves over both, the (expe…
Independent trees are used in building secure and/or fault-tolerant network communication protocols. They have been investigated for different network topologies including tori. Dense Gaussian networks are potential alternatives for 2-dimensional tori. They have similar topological properties; however, they are superiors in carrying communications due to their node-distance distributions and smaller diameters. In this paper, we present constructions of edge-disjoint node-independent spanning trees in dense Gaussian networks. Based on the constructed trees, we design algorithms that could be us…
The metric Ramsey problem asks for the largest subset $S$ of a metric space that can be embedded into an ultrametric (more generally into a Hilbert space) with a given distortion. Study of this problem was motivated as a non-linear version of Dvoretzky theorem. Mendel and Naor 2007 devised the so called Ramsey Partitions to address this problem, and showed the algorithmic applications of their techniques to approximate distance oracles and ranking problems. In this paper we study the natural extension of the metric Ramsey problem to graphs, and introduce the notion of Ramsey Spanning Trees. We…
The article addresses balanced clustering problems with an additional requirement as a tree-like structure over the obtained balanced clusters. This kind of clustering problems can be useful in some applications (e.g., network design, management and routing). Various types of the initial elements are considered. Four basic greedy-like solving strategies (design framework) are considered: balancing-spanning strategy, spanning-balancing strategy, direct strategy, and design of layered structures with balancing. An extended description of the spanning-balancing strategy is presented including fou…
We study a location-routing problem in the context of capacitated vehicle routing. The input is a set of demand locations in a metric space and a fleet of k vehicles each of capacity Q. The objective is to locate k depots, one for each vehicle, and compute routes for the vehicles so that all demands are satisfied and the total cost is minimized. Our main result is a constant-factor approximation algorithm for this problem. To achieve this result, we reduce to the k-median-forest problem, which generalizes both k-median and minimum spanning tree, and which might be of independent interest. We g…
Fully Dynamic Rooted Spanning Tree on GPU
针对现实网络中边插入或删除时维护有根生成森林的挑战，提出四种全动态并行算法，经 GPU 环境实验，其每秒插入和删除吞吐量远超现有并行静态算法。
Given a spatio-temporal network (ST network) where edge properties vary with time, a time-sub-interval minimum spanning tree (TSMST) is a collection of minimum spanning trees of the ST network, where each tree is associated with a time interval. During this time interval, the total cost of tree is least among all the spanning trees. The TSMST problem aims to identify a collection of distinct minimum spanning trees and their respective time-sub-intervals under the constraint that the edge weight functions are piecewise linear. This is an important problem in ST network application domains such …
We introduce the notion of balance for directed graphs: a weighted directed graph is $α$-balanced if for every cut $S \subseteq V$, the total weight of edges going from $S$ to $V\setminus S$ is within factor $α$ of the total weight of edges going from $V\setminus S$ to $S$. Several important families of graphs are nearly balanced, in particular, Eulerian graphs (with $α= 1$) and residual graphs of $(1+ε)$-approximate undirected maximum flows (with $α=O(1/ε)$). We use the notion of balance to give a more fine-grained understanding of several well-studied routing questions that are considerably …
We study a natural problem in graph sparsification, the Spanning Tree Congestion (\STC) problem. Informally, the \STC problem seeks a spanning tree with no tree-edge \emph{routing} too many of the original edges. The root of this problem dates back to at least 30 years ago, motivated by applications in network design, parallel computing and circuit design. Variants of the problem have also seen algorithmic applications as a preprocessing step of several important graph algorithms. For any general connected graph with $n$ vertices and $m$ edges, we show that its STC is at most $\mathcal{O}(\sqr…
In this thesis, Minimal Partitioning (MP) algorithm, an innovative algorithm for enumerating all the spanning trees in an undirected graph is presented. While MP algorithm uses a computational tree graph to traverse all possible spanning trees by the edge exchange technique, it has two unique properties compared to previous algorithms. In the first place, the algorithm maintains a state of minimal partition size in the spanning tree due to edge deletion. This is realized by swapping peripheral edges, more precisely leaf edges, in most of edge exchange operations. Consequently, the main structu…
Given an undirected graph with costs associated with each edge as well as each pair of edges, the quadratic minimum spanning tree problem (QMSTP) consists of determining a spanning tree of minimum total cost. This problem can be used to model many real-life network design applications, in which both routing and interference costs should be considered. For this problem, we propose a three-phase search approach named TPS, which integrates 1) a descent-based neighborhood search phase using two different move operators to reach a local optimum from a given starting solution, 2) a local optima expl…
There is a recent exciting line of work in distributed graph algorithms in the $\mathsf{CONGEST}$ model that exploit expanders. All these algorithms so far are based on two tools: expander decomposition and expander routing. An $(ε,ϕ)$-expander decomposition removes $ε$-fraction of the edges so that the remaining connected components have conductance at least $ϕ$, i.e., they are $ϕ$-expanders, and expander routing allows each vertex $v$ in a $ϕ$-expander to very quickly exchange $\text{deg}(v)$ messages with any other vertices, not just its local neighbors. In this paper, we give the first eff…
The Central Spanning Tree Problem
针对最小生成树与 Steiner 树对噪声敏感的问题，本文提出（分支）中心生成树优化模型及启发式求解方法，统一已有树定义，并在单细胞 RNA 数据和植物三维点云上验证其鲁棒性。
Loss Minimization for Electrical Flows over Spanning Trees on Grids
研究配电网重构问题，证明网格上的NP难性并改进Min-Min算法的近似因子，通过非线性优化分析给出上界。
In this paper we design throughput-optimal dynamic broad- cast algorithms for multi-hop networks with arbitrary topolo- gies. Most of the previous broadcast algorithms route pack- ets along spanning trees, rooted at the source node. For large dynamic networks, computing and maintaining a set of spanning trees is not efficient, as the network-topology may change frequently. In this paper we design a class of dynamic algorithms which makes packet-by-packet schedul- ing and routing decisions and thus obviates the need for maintaining any global topological structures, such as span- ning trees. Ou…
Dynamic programming is a powerful technique that is, unfortunately, often inherently sequential. That is, there exists no unified method to parallelize algorithms that use dynamic programming. In this paper, we attempt to address this issue in the Massively Parallel Computations (MPC) model which is a popular abstraction of MapReduce-like paradigms. Our main result is an algorithmic framework to adapt a large family of dynamic programs defined over trees. We introduce two classes of graph problems that admit dynamic programming solutions on trees. We refer to them as "(polylog)-expressible" an…
The notion of degree-constrained spanning hierarchies, also called k-trails, was recently introduced in the context of network routing problems. They describe graphs that are homomorphic images of connected graphs of degree at most k. First results highlight several interesting advantages of k-trails compared to previous routing approaches. However, so far, only little is known regarding computational aspects of k-trails. In this work we aim to fill this gap by presenting how k-trails can be analyzed using techniques from algorithmic matroid theory. Exploiting this connection, we resolve sever…
We study network design with a cost structure motivated by redundancy in data traffic. We are given a graph, g groups of terminals, and a universe of data packets. Each group of terminals desires a subset of the packets from its respective source. The cost of routing traffic on any edge in the network is proportional to the total size of the distinct packets that the edge carries. Our goal is to find a minimum cost routing. We focus on two settings. In the first, the collection of packet sets desired by source-sink pairs is laminar. For this setting, we present a primal-dual based 2-approximat…
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