Near Optimal Parallel Algorithms for Dynamic DFS in Undirected Graphs

Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently, Baswana et al. [SODA16] presented a simple algorithm for updating DFS tree of an undirected graph after an edge/vertex update in $\tilde{O}(n)$ time. However, their algorithm is strictly sequential. We present an algorithm achieving similar bounds, that can be adopted easily to the parallel environment. In the parallel model, a DFS tree can be computed from scratch using $m$ processors in expected $\tilde{O}(1)$ time [SiComp90] on an EREW PRAM, whereas the best deterministic algorithm takes $\tilde{O}(\sqrt{n})$ time [SiComp90,JAlg93] on a CRCW PRAM. Our algorithm can be used to develop optimal (upto polylog n factors deterministic algorithms for maintaining fully dynamic DFS and fault tolerant DFS, of an undirected graph. 1- Parallel Fully Dynamic DFS: Given an arbitrary online sequence of vertex/edge updates, we can maintain a DFS tree of an undirected graph in $\tilde{O}(1)$ time per update using $m$ processors on an EREW PRAM. 2- Parallel Fault tolerant DFS: An undirected graph can be preprocessed to build a data structure of size O(m) such that for a set of $k$ updates (where $k$ is constant) in the graph, the updated DFS tree can be computed in $\tilde{O}(1)$ time using $n$ processors on an EREW PRAM. Moreover, our fully dynamic DFS algorithm provides, in a seamless manner, nearly optimal (upto polylog n factors) algorithms for maintaining a DFS tree in semi-streaming model and a restricted distributed model. These are the first parallel, semi-streaming and distributed algorithms for maintaining a DFS tree in the dynamic setting.Comment: Accepted to appear in SPAA'17, 32 Pages, 5 Figure

Robustness: a New Form of Heredity Motivated by Dynamic Networks

We investigate a special case of hereditary property in graphs, referred to as {\em robustness}. A property (or structure) is called robust in a graph $G$ if it is inherited by all the connected spanning subgraphs of $G$. We motivate this definition using two different settings of dynamic networks. The first corresponds to networks of low dynamicity, where some links may be permanently removed so long as the network remains connected. The second corresponds to highly-dynamic networks, where communication links appear and disappear arbitrarily often, subject only to the requirement that the entities are temporally connected in a recurrent fashion ({\it i.e.} they can always reach each other through temporal paths). Each context induces a different interpretation of the notion of robustness. We start by motivating the definition and discussing the two interpretations, after what we consider the notion independently from its interpretation, taking as our focus the robustness of {\em maximal independent sets} (MIS). A graph may or may not admit a robust MIS. We characterize the set of graphs \forallMIS in which {\em all} MISs are robust. Then, we turn our attention to the graphs that {\em admit} a robust MIS (\existsMIS). This class has a more complex structure; we give a partial characterization in terms of elementary graph properties, then a complete characterization by means of a (polynomial time) decision algorithm that accepts if and only if a robust MIS exists. This algorithm can be adapted to construct such a solution if one exists

Implicit Decomposition for Write-Efficient Connectivity Algorithms

The future of main memory appears to lie in the direction of new technologies that provide strong capacity-to-performance ratios, but have write operations that are much more expensive than reads in terms of latency, bandwidth, and energy. Motivated by this trend, we propose sequential and parallel algorithms to solve graph connectivity problems using significantly fewer writes than conventional algorithms. Our primary algorithmic tool is the construction of an $o(n)$-sized "implicit decomposition" of a bounded-degree graph $G$ on $n$ nodes, which combined with read-only access to $G$ enables fast answers to connectivity and biconnectivity queries on $G$. The construction breaks the linear-write "barrier", resulting in costs that are asymptotically lower than conventional algorithms while adding only a modest cost to querying time. For general non-sparse graphs on $m$ edges, we also provide the first $o(m)$ writes and $O(m)$ operations parallel algorithms for connectivity and biconnectivity. These algorithms provide insight into how applications can efficiently process computations on large graphs in systems with read-write asymmetry

Increasing the density of available pareto optimal solutions

The set of available multi-objective optimization algorithms continues to grow. This fact can be partially attributed to their widespread use and applicability. However this increase also suggests several issues remain to be addressed satisfactorily. One such issue is the diversity and the number of solutions available to the decision maker (DM). Even for algorithms very well suited for a particular problem, it is difficult - mainly due to the computational cost - to use a population large enough to ensure the likelihood of obtaining a solution close to the DMs preferences. In this paper we present a novel methodology that produces additional Pareto optimal solutions from a Pareto optimal set obtained at the end run of any multi-objective optimization algorithm. This method, which we refer to as Pareto estimation, is tested against a set of 2 and 3-objective test problems and a 3-objective portfolio optimization problem to illustrate its’ utility for a real-world problem

Modeling Financial Time Series with Artificial Neural Networks

Financial time series convey the decisions and actions of a population of human actors over time. Econometric and regressive models have been developed in the past decades for analyzing these time series. More recently, biologically inspired artificial neural network models have been shown to overcome some of the main challenges of traditional techniques by better exploiting the non-linear, non-stationary, and oscillatory nature of noisy, chaotic human interactions. This review paper explores the options, benefits, and weaknesses of the various forms of artificial neural networks as compared with regression techniques in the field of financial time series analysis.CELEST, a National Science Foundation Science of Learning Center (SBE-0354378); SyNAPSE program of the Defense Advanced Research Project Agency (HR001109-03-0001

An oil pipeline design problem

Copyright @ 2003 INFORMSWe consider a given set of offshore platforms and onshore wells producing known (or estimated) amounts of oil to be connected to a port. Connections may take place directly between platforms, well sites, and the port, or may go through connection points at given locations. The configuration of the network and sizes of pipes used must be chosen to minimize construction costs. This problem is expressed as a mixed-integer program, and solved both heuristically by Tabu Search and Variable Neighborhood Search methods and exactly by a branch-and-bound method. Two new types of valid inequalities are introduced. Tests are made with data from the South Gabon oil field and randomly generated problems.The work of the first author was supported by NSERC grant #OGP205041. The work of the second author was supported by FCAR (Fonds pour la Formation des Chercheurs et l’Aide à la Recherche) grant #95-ER-1048, and NSERC grant #GP0105574