On the Power of Priority Algorithms for Facility Location and Set Cover

Angelopoulos, Spyros; Borodin, Allan

doi:10.1007/3-540-45753-4_5

Cited by 21 publications

(44 citation statements)

References 13 publications

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“…Proof Lemma 11 guarantees a single graph G for which the result of the 2 n 1/9 -improbability game is uniquely extendible with probability 1 − o (1). The theorem now follows directly from Lemma 4.…”

Section: Theorem 12mentioning

confidence: 61%

“…By Lemmas 9,8, and 10 the probability that the partial information PI and the partial solution PS will violate any of the invariants is: e − (t) + e − (t) + e − (tpn) = o (1). Hence with probability 1 − o(1) at the end of the Q-improbability game the partial instance is uniquely extendible.…”

Section: Lemma 11mentioning

confidence: 96%

“…1 . v must be on the path from the root to the unique solution in H , and the value returned along this path must be 1.…”

Section: Lower Bounds For Perfect Matching Problem In Bipartite Graphsmentioning

confidence: 99%

“…We build on the framework established by Borodin, Nielsen and Rackoff [7], called priority algorithms, and subsequently studied and generalized by [1,2,8,9,12,17], among others. Various versions of these models succeed in capturing large classes of greedy, dynamic programming, backtracking, and primal-dual algorithms, but they also allow either impossibility results or strong complexity lower bounds to be proven for natural problems that should not intuitively fit the models.…”

Section: Introductionmentioning

confidence: 99%

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A Stronger Model of Dynamic Programming Algorithms

2010

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We define a formal model of dynamic programming algorithms which we call Prioritized Branching Programs (pBP). Our model is a generalization of the BT model of Alekhnovich et al. (IEEE Conference on Computational Complexity, pp. 308-322, 2005), which is in turn a generalization of the priority algorithms model of Borodin, Nielson and Rackoff. One of the distinguishing features of these models is that they not only capture large classes of algorithms generally considered to be greedy, backtracking or dynamic programming algorithms, but they also allow characterizations of their limitations. Hence they give meaning to the statement that a given problem can or cannot be solved by dynamic programming. After defining the model, we prove three main results: (i) that certain types of natural restrictions of our seemingly more powerful model can be simulated by the BT model; (ii) that in general our model is stronger than the BT model-a fact which is witnessed by the classical shortest paths problem; (iii) that our model has very real limitations, namely that bipartite matching cannot be efficiently computed in it, hence suggesting that there are problems that can be solved efficiently by network flow algorithms and by simple linear programming that cannot be solved by natural dynamic programming approaches.S.

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Section: Theorem 12mentioning

confidence: 61%

Section: Lemma 11mentioning

confidence: 96%

“…1 . v must be on the path from the root to the unique solution in H , and the value returned along this path must be 1.…”

Section: Lower Bounds For Perfect Matching Problem In Bipartite Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Stronger Model of Dynamic Programming Algorithms

2010

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“…For any of the problems already studied in the priority framework (e.g. Angelopoulos & Borodin 2004;Borodin et al 2003Borodin et al , 2005Davis & Impagliazzo 2009;Regev 2002) it would be interesting to consider constant-width pBT algorithms. Our only general approximation-width tradeoff results are the somewhat complementary upper and lower bounds for the knapsack problem and the fixed-order lower bound for interval scheduling for which (as noted above) we do not have a complementary upper bound.…”

Section: Open Questionsmentioning

confidence: 99%

Toward a Model for Backtracking and Dynamic Programming

et al. 2011

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We propose a model called priority branching trees (pBT ) for backtracking and dynamic programming algorithms. Our model generalizes both the priority model of Borodin, Nielson and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence spans a wide spectrum of algorithms. After witnessing the strength of the model, we then show its limitations by providing lower bounds for algorithms in this model for several classical problems such as Interval Scheduling, Knapsack and Satisfiability.

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