This article focuses on the problem of coflow scheduling with precedence constraints in identical parallel networks, a well-known NP -hard problem. Coflow is a relatively new network abstraction that characterizes com...
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This article focuses on the problem of coflow scheduling with precedence constraints in identical parallel networks, a well-known NP -hard problem. Coflow is a relatively new network abstraction that characterizes communication patterns in data centers. When considering workload sizes and weights that are dependent on the network topology in the input instances, the proposed algorithm for the flow-level scheduling problem achieves an approximation ratio of O(chi) where chi is the coflow number of the longest path in the directed acyclic graph (DAG). Additionally, when taking into account topology-dependent workload sizes, the algorithm achieves an approximation ratio of O(R chi) , where R represents the ratio of maximum weight to minimum weight. For the coflow-level scheduling problem, the proposed algorithm achieves an approximation ratio of O(m chi) , where m is the number of network cores when considering workload sizes and weights that are topology-dependent. Moreover, when considering topology-dependent workload sizes, the algorithm achieves an approximation ratio of O(Rm chi) . In the coflows of multi-stage job scheduling problem, the proposed algorithm achieves an approximation ratio of O(chi) . Although our theoretical results are based on a limited set of input instances, experimental findings show that the results for general input instances outperform the theoretical results.
We study routing problems of a convoy in a graph, generalizing the shortest path problem (SPP), the travelling salesperson problem (TSP), and the Chinese postman problem (CPP) which are all well-studied in the classic...
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We study routing problems of a convoy in a graph, generalizing the shortest path problem (SPP), the travelling salesperson problem (TSP), and the Chinese postman problem (CPP) which are all well-studied in the classical (non-convoy) setting. We assume that each edge in the graph has a length and a speed at which it can be traversed and that our convoy has a given length. While the convoy moves through the graph, parts of it can be located on different edges. For safety requirements, at all time the whole convoy needs to travel at the same speed which is dictated by the slowest edge on which currently a part of the convoy is located. For Convoy-SPP, we give a strongly polynomial time exact algorithm. For Convoy-TSP, we provide an O(logn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\log n)$$\end{document}-approximation algorithm and an O(1)-approximation algorithm for trees. Both results carry over to Convoy-CPP which-maybe surprisingly-we prove to be NP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{NP}$$\end{document}-hard in the convoy setting. This contrasts the non-convoy setting in which the problem is polynomial time solvable.
We study the approximability of the Longest Run Subsequence problem (LRS for short). For a string S = s1 · · · sn over an alphabet Σ, a run of a symbol σ ∈ Σ in S is a maximal substring of consecuti...
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It is known that one-dimensional variable-sized bin packing problem and network optimization problem are classical combinatorial optimization problems. Inspired by this, we consider a new problem of variable-sized mat...
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In clustering problems, one has to partition a given set of objects into pairwise disjoint subsets (clusters) taking into account only similarity of objects. In the graph cluster editing problem similarity relation on...
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Classical network design models, such as the Survivable Network Design problem (SNDP), are (partly) motivated by robustness to faults under the assumption that any subset of edges upto a specific number can fail. We c...
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ISBN:
(纸本)9783959772785
Classical network design models, such as the Survivable Network Design problem (SNDP), are (partly) motivated by robustness to faults under the assumption that any subset of edges upto a specific number can fail. We consider non-uniform fault models where the subset of edges that fail can be specified in different ways. Our primary interest is in the flexible graph connectivity model [1, 3, 4, 8], in which the edge set is partitioned into safe and unsafe edges. Given parameters p, q ≥ 1, the goal is to find a cheap subgraph that remains p-connected even after the failure of q unsafe edges. We also discuss the bulk-robust model [6, 2] and the relative survivable network design model [19]. While SNDP admits a 2-approximation [32], the approximability of problems in these more complex models is much less understood even in special cases. We make two contributions. Our first set of results are in the flexible graph connectivity model. Motivated by a conjecture that a constant factor approximation is feasible when p and q are fixed, we consider two special cases. For the s-t case we obtain an approximation ratio that depends only on p, q whenever p + q > pq/2 which includes (p, 2) and (2, q) for all p, q ≥ 1. For the global connectivity case we obtain an O(q) approximation for (2, q), and an O(p) approximation for (p, 2) and (p, 3) for any p ≥ 1, and for (p, 4) when p is even. These are based on an augmentation framework and decomposing the families of cuts that need to be covered into a small number of uncrossable families. Our second result is a poly-logarithmic approximation for a generalization of the bulk-robust model when the "width" of the given instance (the maximum number of edges that can fail in any particular scenario) is fixed. Via this, we derive corresponding approximations for the flexible graph connectivity model and the relative survivable network design model. We utilize a recent framework due to Chen et al. [17] that was designed for handling group co
We give a polynomial-time(formula presented)-approximation algorithm for minimum-time broadcast and minimum-time multicast in n-node networks under the single-port vertex-disjoint paths mode. This improves a previous ...
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We study the classic weighted maximum throughput problem on unrelated machines. We give a (1 − 1/e − Ε)-approximation algorithm for the preemptive case. To our knowledge this is the first ever approximation result fo...
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Graph Burning models information spreading in a given graph as a process such that in each step one node is infected (informed) and also the infection spreads to all neighbors of previously infected nodes. Formally, g...
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We study Dominating Set and Independent Set for dynamic graphs in the vertex- arrival model. We say that a dynamic algorithm for one of these problems is k-stable when it makes at most k changes to its output independ...
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