Let G = (V, E) be a complete undirected graph with vertex set V, edge set E and let H = be a hypergraph, where S is a set of not necessarily disjoint clusters S1, …, Sm, Si ⊆ V ∀i ∈ {1, …, m}. The clustered traveli...
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We revisit the problem of online linear optimization in case the set of feasible actions is accessible through an approximated linear optimization oracle with a factor alpha multiplicative approximation guarantee. Thi...
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We revisit the problem of online linear optimization in case the set of feasible actions is accessible through an approximated linear optimization oracle with a factor alpha multiplicative approximation guarantee. This setting is in particular interesting since it captures natural online extensions of well-studied offline linear optimization problems which are NP-hard, yet admit efficient approximation algorithms. The goal here is to minimize the alpha-regret which is the natural extension of the standard regret in online learning to this setting. We present new algorithms with significantly improved oracle complexity for both the full information and bandit variants of the problem. Mainly, for both variants, we present alpha-regret bounds of O(T-1/3), were T is the number of prediction rounds, using only O(log(T)) calls to the approximation oracle per iteration, on average. These are the first results to obtain both average oracle complexity of O(log(T)) (or even poly-logarithmic in T) and alpha-regret bound O(T-c) for a constant c > 0, for both variants.
This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size n subject to a knapsack constraint...
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ISBN:
(纸本)9781956792034
This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size n subject to a knapsack constraint, DLA and RLA. DLA is a deterministic algorithm that provides an approximation factor of 6+epsilon while RLA is a randomized algorithm with an approximation factor of 4+epsilon. Both run in O(n log(1/epsilon)/epsilon) query complexity. The key idea to obtain a constant approximation ratio with linear query lies in: (1) dividing the ground set into two appropriate subsets to find the near-optimal solution over these subsets with linear queries, and (2) combining a threshold greedy with properties of two disjoint sets or a random selection process to improve solution quality. In addition to the theoretical analysis, we have evaluated our proposed solutions with three applications: Revenue Maximization, Image Summarization, and Maximum Weighted Cut, showing that our algorithms not only return comparative results to state-of-the-art algorithms but also require significantly fewer queries.
In the well-studied Unsplittable Flow on a Path problem (UFP), we are given a path graph with edge capacities. Furthermore, we are given a collection of n tasks, each one characterized by a sub path, a weight, and a d...
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ISBN:
(纸本)9783319286846;9783319286839
In the well-studied Unsplittable Flow on a Path problem (UFP), we are given a path graph with edge capacities. Furthermore, we are given a collection of n tasks, each one characterized by a sub path, a weight, and a demand. Our goal is to select a maximum weight subset of tasks so that the total demand of selected tasks using each edge is upper bounded by the corresponding capacity. Chakaravarthy et al. [ESA'14] studied a generalization of UFP, bagUFP, where tasks are partitioned into bags, and we can select at most one task per bag. Intuitively, bags model jobs that can be executed at different times (with different duration, weight, and demand). They gave a 0(log n) approximation for bagUFP. This is also the best known ratio in the case of uniform weights. In this paper we achieve the following main results:
We consider the distributed construction of a minimum weight 2edge-connected spanning subgraph (2-ECSS) of a given weighted or unweighted graph. A 2-ECSS of a graph is a subgraph that, for each pair of vertices, conta...
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ISBN:
(数字)9783540770961
ISBN:
(纸本)9783540770954
We consider the distributed construction of a minimum weight 2edge-connected spanning subgraph (2-ECSS) of a given weighted or unweighted graph. A 2-ECSS of a graph is a subgraph that, for each pair of vertices, contains at least two edge-disjoint paths connecting these vertices. The problem of finding a minimum weight 2-ECSS is NP-hard and a natural extension of the distributed MST construction problem, one of the most fundamental problems in the area of distributed computation. We present a distributed 3/2-approximation algorithm for the unweighted 2-ECSS construction problem that requires O(n) communication rounds and O(m) messages. Moreover, we present a distributed 3-approximation algorithm for the weighted 2-ECSS construction problem that requires O(nlogn) communication rounds and O(nlog(2)n+m) messages.
A top-list is a possibly incomplete ranking of elements: only a subset of the elements are ranked, with all unranked elements tied for last. Top-list aggregation, a generalization of the well-known rank aggregation pr...
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ISBN:
(纸本)9781611975994
A top-list is a possibly incomplete ranking of elements: only a subset of the elements are ranked, with all unranked elements tied for last. Top-list aggregation, a generalization of the well-known rank aggregation problem, takes as input a collection of top-lists and aggregates them into a single complete ranking, aiming to minimize the number of upsets (pairs ranked in opposite order in the input and in the output). In this paper, we give simple approximation algorithms for top-list aggregation. We generalize the footrule algorithm for rank aggregation (which minimizes Spearman's footrule distance), yielding a simple 2-approximation algorithm for top-list aggregation. Ailon's REPEATCHOICE algorithm for bucket-orders aggregation yields a 2-approximation algorithm for top-list aggregation. Using inspiration from approval voting, we define the score of an element as the frequency with which it is ranked, i.e. appears in an input top-list. We reinterpret REPEATCHOICE for top-list aggregation as a randomized algorithm using variables whose expectations correspond to score and to the average rank of an element given that it is ranked. Using average ranks, we generalize and analyze Borda's algorithm for rank aggregation. We observe that the natural generalization is not a constant approximation. We design a simple 2-phase variant of the Generalized Borda's algorithm, roughly sorting by scores and breaking ties by average ranks, yielding another simple constant-approximation algorithm for top-list aggregation. We then design another 2-phase variant in which in order to break ties we use, as a black box, the Mathieu-Schudy PTAS for rank aggregation, yielding a PTAS for top-list aggregation. This solves an open problem posed by Ailon. Finally, in the special case in which all input lists have length at most k, we design another simple 2-phase algorithm based on sorting by scores, and prove that it is an EPTAS - the complexity is O(n log n) when k = o(logn).
In this paper we consider both the maximization variant MAX REP and the minimization variant MIN REP of the famous LABEL COVER. problem, for which, till now, the best approximation ratios known were O(root n). In fact...
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ISBN:
(纸本)9783642041273
In this paper we consider both the maximization variant MAX REP and the minimization variant MIN REP of the famous LABEL COVER. problem, for which, till now, the best approximation ratios known were O(root n). In fact, several recent papers reduced LABEL COVER to other problems, arguing that if better approximation algorithms for their problems existed, then a wo(root n)-approximation algorithm for LABEL COVER. would exist. We show, in fact, that there are a O(n(1/3))-approximation algorithm for MAX REP and a O(n(1/3) log(2/3) n)-approximation algorithm for MIN REP. In addition, we also exhibit a randomized reduction from DENSEST kappa-SUBGRAPH to MAX REP, showing that any approximation factor for MAX REP implies the same factor (up to a constant) for DENSEST kappa-SUBGRAPH.
We study parameterized algorithms and approximation algorithms for the maximum agreement forest problem, which, for two given leaf-labeled trees, is to find a maximum forest that is a subgraph of both trees. The probl...
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ISBN:
(纸本)9783642450433
We study parameterized algorithms and approximation algorithms for the maximum agreement forest problem, which, for two given leaf-labeled trees, is to find a maximum forest that is a subgraph of both trees. The problem was motivated by the research in phylogenetics. For parameterized algorithms, while the problem is known to be fixed-parameter tractable for binary trees, it was an open problem whether the problem is still fixed-parameter tractable for general trees. We resolve this open problem by developing an O(3(k)n)-time parameterized algorithm for the problem on general trees. Our techniques on tree structures also lead to a polynomial-time approximation algorithm of ratio 3 for the problem, giving the first constant-ratio approximation algorithm for the problem on general trees.
We resolve the fundamental problem of online decoding with general nth order ergodic Markov chain models. Specifically, we provide deterministic and randomized algorithms whose performance is close to that of the opti...
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We resolve the fundamental problem of online decoding with general nth order ergodic Markov chain models. Specifically, we provide deterministic and randomized algorithms whose performance is close to that of the optimal offline algorithm even when latency is small. Our algorithms admit efficient implementation via dynamic programs, and readily extend to (adversarial) non-stationary or time-varying settings. We also establish lower bounds for online methods under latency constraints in both deterministic and randomized settings, and show that no online algorithm can perform significantly better than our algorithms. To our knowledge, our work is the first to analyze general Markov chain decoding under hard constraints on latency. We provide strong empirical evidence to illustrate the potential impact of our work in applications such as gene sequencing.
This paper presents the design and analysis of parallel approximation algorithms for facility-location problems, including NC and RNC algorithms for (metric) facility location, k-center, k-median, and k-means These pr...
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ISBN:
(纸本)9781450300797
This paper presents the design and analysis of parallel approximation algorithms for facility-location problems, including NC and RNC algorithms for (metric) facility location, k-center, k-median, and k-means These problems have received considerable attention during the past decades from the approximation algorithms community, which primarily concentrates on improving the approximation guarantees In this paper, we ask. Is it possible to parallelize some of the beautiful results from the sequential setting? Our starting point is a small, but diverse, subset of results in approximation algorithms for facility-location problems, with a primary goal of developing techniques for devising their efficient parallel counterparts. We focus on giving algorithms with low depth, near work efficiency (compared to the sequential versions), and low cache complexity
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