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Applying parallel computation algorithms in the design of serial algorithms
 J. ACM
, 1983
"... Abstract. The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for design ..."
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Cited by 234 (7 self)
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Abstract. The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for designing an efficient serial algorithm for another problem. A d ~ eframework d for cases like this is presented. Particular cases, which are discussed in this paper, provide motivation for examining parallelism in sorting, selection, minimumspanningtree, shortest route, maxflow, and matrix multiplication problems, as well as in scheduling and locational problems.
Improved Orientations of Physical Networks
"... Abstract. The orientation of physical networks is a prime task in deciphering the signalingregulatory circuitry of the cell. One manifestation of this computational task is as a maximum graph orientation problem, where given an undirected graph on n vertices and a collection of vertex pairs, the go ..."
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Cited by 12 (4 self)
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Abstract. The orientation of physical networks is a prime task in deciphering the signalingregulatory circuitry of the cell. One manifestation of this computational task is as a maximum graph orientation problem, where given an undirected graph on n vertices and a collection of vertex pairs, the goal is to orient the edges of the graph so that a maximum number of pairs are connected by a directed path. We develop a novel approximation algorithm for this problem with a performance guarantee of O(logn/loglogn), improving on the current logarithmic approximation. In addition, motivated by interactions whose direction is preset, such as proteinDNA interactions, we extend our algorithm to handle mixed graphs, a major open problem posed by earlier work. In this setting, we show that a polylogarithmic approximation ratio is achievable under biologicallymotivated assumptions on the sought paths. 1
A sublogarithmic approximation for highway and tollbooth pricing
 In Proceedings of the 37th International Colloquium on Automata, Languages and Programming
, 2010
"... An instance of the tollbooth problem consists of an undirected network and a collection of singleminded customers, each of which is interested in purchasing a fixed path subject to an individual budget constraint. The objective is to assign a perunit price to each edge in a way that maximizes the c ..."
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Cited by 10 (2 self)
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An instance of the tollbooth problem consists of an undirected network and a collection of singleminded customers, each of which is interested in purchasing a fixed path subject to an individual budget constraint. The objective is to assign a perunit price to each edge in a way that maximizes the collective revenue obtained from all customers. The revenue generated by any customer is equal to the overall price of the edges in her desired path, when this cost falls within her budget; otherwise, that customer will not purchase any edge. Our main result is a deterministic algorithm for the tollbooth problem on trees whose approximation ratio is O(log m / log log m), where m denotes the number of edges in the underlying graph. This finding improves on the currently best performance guarantees for trees, due to Elbassioni et al. (SAGT ’09), as well as for paths (commonly known as the highway problem), due to Balcan and Blum (EC ’06). An additional interesting consequence is a computational separation between tollbooth pricing on trees and the original prototype problem of singleminded unlimited supply pricing, under a plausible hardness hypothesis due to Demaine et al. (SODA ’06).
Approximation Algorithms for Orienting Mixed Graphs
"... Abstract. Graph orientation is a fundamental problem in graph theory that has recently arisen in the study of signalingregulatory pathways in protein networks. Given a graph and a list of ordered sourcetarget vertex pairs, it calls for assigning directions to the edges of the graph so as to maximi ..."
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Cited by 8 (2 self)
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Abstract. Graph orientation is a fundamental problem in graph theory that has recently arisen in the study of signalingregulatory pathways in protein networks. Given a graph and a list of ordered sourcetarget vertex pairs, it calls for assigning directions to the edges of the graph so as to maximize the number of pairs that admit a directed sourcetotarget path. When the input graph is undirected, a sublogarithmic approximation is known for the problem. However, the approximability of the biologicallyrelevant variant, in which the input graph has both directed and undirected edges, was left open. Here we give the first approximation algorithm to this problem. Our algorithm provides a sublinear guarantee in the general case, and logarithmic guarantees for structured instances. Key words: proteinprotein interaction network, mixed graph, graph orientation, approximation algorithm 1
Robust Subgraphs for Trees and Paths ∗
"... Consider a graph problem which is associated with a parameter, for example, that of finding a longest tour spanning k vertices. The following question is natural: Is there a small subgraph which contains an optimal or near optimal solution for every possible value of the given parameter? Such a subg ..."
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Cited by 2 (2 self)
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Consider a graph problem which is associated with a parameter, for example, that of finding a longest tour spanning k vertices. The following question is natural: Is there a small subgraph which contains an optimal or near optimal solution for every possible value of the given parameter? Such a subgraph is said to be robust. In this paper we consider the problems of finding heavy paths and heavy trees of k edges. In these two cases we prove surprising bounds on the size of a robust subgraph for a variety of approximation ratios. For both problems we show that in every complete weighted graph on n vertices α there exists a subgraph with approximately 1−α2 n edges which contains an αapproximate solution for every k = 1,..., n − 1. In the analysis of the tree problem we also describe a new result regarding balanced decomposition of trees. In addition, we consider variations in which the subgraph itself is restricted to be a path or a tree. For these problems we describe polynomial time algorithms and corresponding proofs of negative results. 1
On the Approximability of Reachability Preserving Network Orientations ∗
"... We introduce a graph orientation problem arising in the study of biological networks. Given an undirected graph and a list of ordered sourcetarget vertex pairs, the goal is to orient the graph such that a maximum number of pairs admit a directed sourcetotarget path. We study the complexity and ap ..."
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We introduce a graph orientation problem arising in the study of biological networks. Given an undirected graph and a list of ordered sourcetarget vertex pairs, the goal is to orient the graph such that a maximum number of pairs admit a directed sourcetotarget path. We study the complexity and approximability of this problem. We show that the problem is NPhard even on star graphs and hard to approximate to within some constant factor. On the positive side, we provide an Ω(loglogn/logn)factor approximation algorithm for the problem on nvertex graphs. We further show that for any instance of the problem there exists an orientation of the input graph that satisfies a logarithmic fraction of all pairs and that this bound is tight up to a constant factor. Our techniques also lead to constant factor approximation algorithms for some restricted variants of the problem. Key words: network orientation, graph orientation, approximation algorithm, biological network, proteinprotein interaction 1
Approximation Algorithms for Orienting Mixed Graphs ✩
"... Graph orientation is a fundamental problem in graph theory that has recently arisen in the study of signalingregulatory pathways in protein networks. Given a graph and a list of sourcetarget vertex pairs, one wishes to assign directions to the edges so as to maximize the number of pairs that admit ..."
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Graph orientation is a fundamental problem in graph theory that has recently arisen in the study of signalingregulatory pathways in protein networks. Given a graph and a list of sourcetarget vertex pairs, one wishes to assign directions to the edges so as to maximize the number of pairs that admit a directed sourcetotarget path. When the input graph is undirected, a sublogarithmic approximation is known for this problem. However, the approximability of the biologicallyrelevant variant, in which the input graph has both directed and undirected edges, was left open. Here we give the first approximation algorithms to this problem. Our algorithms provide a sublinear guarantee in the general case, and logarithmic guarantees for structured instances. Key words: proteinprotein interaction network, mixed graph, graph orientation, approximation algorithm 1.