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Submodular Unsplittable Flow on Trees [chapter]

Anna Adamaszek, Parinya Chalermsook, Alina Ene, Andreas Wiese
2016 Lecture Notes in Computer Science  
We study the Unsplittable Flow problem (UFP) on trees with a submodular objective function.  ...  (Amazing 2+ approximation for unsplittable flow on a path, SIAM, pp 26-41, 2014) for UFP on paths with a linear objective.  ...  ( j, +), i( j, −), -if we select exactly one task corresponding to each clause (no matter which one) and exactly one task corresponding to each variable then we do not violate the edge capacities on the  ... 
doi:10.1007/978-3-319-33461-5_28 fatcat:faw7ehs2hrfilldok5k5ezjqim

Submodular unsplittable flow on trees

Anna Adamaszek, Parinya Chalermsook, Alina Ene, Andreas Wiese
2018 Mathematical programming  
We study the Unsplittable Flow problem (UFP) on trees with a submodular objective function.  ...  Our main result is an O(k log n)-approximation algorithm for Submodular UFP on trees where k denotes the pathwidth of the given tree.  ...  ( j, +), i( j, −), -if we select exactly one task corresponding to each clause (no matter which one) and exactly one task corresponding to each variable then we do not violate the edge capacities on the  ... 
doi:10.1007/s10107-017-1218-4 fatcat:qx5vifr3xbe4xhka4zq6ip4m2q

Page 2350 of Mathematical Reviews Vol. , Issue 2000c [page]

2000 Mathematical Reviews  
, Masataka Nakamura and Takashi Takabatake, Integral polyhedra associated with certain submodular functions defined on 012-vectors (289-303).  ...  Kolliopoulos and Clifford Stein, Experimental evaluation of approximation algorithms for single- source unsplittable flow (328-344); Vardges Melkonian and Eva Tardos, Approximation algorithms for a directed  ... 

A NOTE ON MULTIFLOW LOCKING THEOREM

Hiroshi Hirai
2010 Journal of the Operations Research Society of Japan  
In fact, it is known that every laminar partial cut family is obtained by a family of subtrees on a tree in this way [9] . it is exactly a nonnegative sum of cut distances for a laminar partial cut family  ...  Let .A be a set of partial cuts on T, Fbr a multifiow f, we say " f tocks .4'; if f is a maximum (A,B)-flow for all (A,B) E v4.  ... 
doi:10.15807/jorsj.53.149 fatcat:3rq6n5rx6fhdhouq5dslkrjd74

Algorithms to Approximate Column-Sparse Packing Problems [chapter]

Brian Brubach, Karthik A. Sankararaman, Aravind Srinivasan, Pan Xu
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
., Algorithmica, 2012), and go "half the remaining distance" to optimal for a major integrality-gap conjecture of Füredi, Kahn and Seymour on hypergraph matching (Combinatorica, 1993).  ...  Additionally, we show a simple application of simulation-based attenuation to obtain improved ratios for the Unsplittable Flow Problem on trees (UFP-TREES: Chekuri et al.  ...  We show that by incorporating simple attenuation ideas, we can improve the analysis of the previous best algorithm for the Unsplittable Flow Problem in Trees (UFP-TREES) with unit demands and non-negative  ... 
doi:10.1137/1.9781611975031.22 dblp:conf/soda/BrubachSSX18 fatcat:xluk5r7or5hvdbvodypvmqifgy

Algorithms to Approximate Column-Sparse Packing Problems [article]

Brian Brubach, Karthik Abinav Sankararaman, Aravind Srinivasan, Pan Xu
2019 arXiv   pre-print
., Algorithmica, 2012), and go "half the remaining distance" to optimal for a major integrality-gap conjecture of Furedi, Kahn and Seymour on hypergraph matching (Combinatorica, 1993).  ...  We also thank him for pointing out useful prior results on graph coloring in parallel and distributed settings. We would like to thank the anonymous reviewers for valuable comments on this paper.  ...  Additionally, we show a simple application of simulation-based attenuation to obtain improved ratios for the Unsplittable Flow Problem on trees (UFP-TREES: Chekuri et al.  ... 
arXiv:1711.02724v6 fatcat:d6yiu6bqbjdslmvosgjgrqlmqe

Welfare Maximization with Deferred Acceptance Auctions in Reallocation Problems [article]

Anthony Kim
2015 arXiv   pre-print
In these problems, while the "allocated" agents transact, exchanging rights and payments, the objective and feasibility constraints are on the "rejected" agents.  ...  In the multicast routing version of the problem, each firm has a set of terminal vertices, with one being the source, and demands a (unsplittable) multicast tree (a.k.a., Steiner tree) spanning the terminals  ...  flow of the demanded amount between terminals subject to the edge capacity constraints.  ... 
arXiv:1507.01353v3 fatcat:5xfkktestrgslkira4rap6vypq

Stochastic Vehicle Routing with Recourse [article]

Inge Li Goertz, Viswanath Nagarajan, Rishi Saket
2012 arXiv   pre-print
Finally, we provide a Unique Games Conjecture based omega(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.  ...  The main idea in this result is relating StochVRP to a special case of submodular orienteering, called knapsack rank-function orienteering.  ...  V \ S) + Flow(V \ S) where for any T ⊆ V , MST(T ) = length of minimum spanning tree on {r} T , and Flow(T ) := 1 Q v∈T q v · d(r, v).  ... 
arXiv:1202.5797v2 fatcat:k54fofyjo5genedauh522l6bbu

Multi-dimensional mechanism design via random order contention resolution schemes

Marek Adamczyk, Michał Włodarczyk
2020 ACM SIGecom Exchanges  
The paper left open the question on how to obtain a constant approximation for the matroid setting.  ...  The seminal work of [Chawla et al. 2009] on sequential posted pricing mechanisms gave us an approach for approximately solving the Bayesian multi-parameter unitdemand mechanism design problem (BMUMD).  ...  unsplittable flows on trees.  ... 
doi:10.1145/3381329.3381334 fatcat:uqh7sjhjarfeplrjryyvtl4thu

Submodular function maximization via the multilinear relaxation and contention resolution schemes

Jan Vondrák, Chandra Chekuri, Rico Zenklusen
2011 Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11  
Our algorithms are based on (approximately) solving the multilinear extension F of f [5] over a polytope P that represents the constraints, and then effectively rounding the fractional solution.  ...  Our results provide a broadly applicable framework for maximizing linear and submodular functions subject to independence constraints. We give several illustrative examples.  ...  Acknowledgments: We thank Mohit Singh for helpful discussions on contention resolution schemes for matroids.  ... 
doi:10.1145/1993636.1993740 dblp:conf/stoc/VondrakCZ11 fatcat:mqevhorqgfecjhj73gxbtbw3jy

Submodular Function Maximization via the Multilinear Relaxation and Contention Resolution Schemes

Chandra Chekuri, Jan Vondrák, Rico Zenklusen
2014 SIAM journal on computing (Print)  
Our algorithms are based on (approximately) solving the multilinear extension F of f [5] over a polytope P that represents the constraints, and then effectively rounding the fractional solution.  ...  Our results provide a broadly applicable framework for maximizing linear and submodular functions subject to independence constraints. We give several illustrative examples.  ...  Acknowledgments: We thank Mohit Singh for helpful discussions on contention resolution schemes for matroids.  ... 
doi:10.1137/110839655 fatcat:a3cz23jdzfbttjdwfkbyofxypa

A Mazing 2+ε Approximation for Unsplittable Flow on a Path

Aris Anagnostopoulos, Fabrizio Grandoni, Stefano Leonardi, Andreas Wiese
2018 ACM Transactions on Algorithms  
The problem of unsplittable flow on a tree (UFT) is the generalization of UFP where the input graph is a tree rather than a path.  ...  A Mazing 2+ Approximation for Unsplittable Flow on a Path 1:3 ( ) ( ) ( ) ( ) Fig. 1.  ... 
doi:10.1145/3242769 fatcat:m6wmtvangfc5lbgaogxnmlpe3a

A Theoretical Examination of Practical Game Playing: Lookahead Search [chapter]

Vahab Mirrokni, Nithum Thain, Adrian Vetta
2012 Lecture Notes in Computer Science  
Unsplittable Selfish Routing Now consider the unsplittable selfish routing game. We show that any 2-lookahead equilibrium has a constant coordination ratio.  ...  Then G is a valid-utility game if it satisfies the following properties: (1) Submodular and Non-decreasing Social Function: The corresponding set function for γ is submodular and non-decreasing. (2) Vickrey  ...  Unsplittable Selfish Routing Proof of Theorem 4.1. This proof adapts the result in [3] to our setting. Let f be any flow at a lookahead equilibrium and f * be an optimal flow.  ... 
doi:10.1007/978-3-642-33996-7_22 fatcat:z2geyw4aszcmpa5bwynfepr5cq

Submodular Function Maximization via the Multilinear Relaxation and Contention Resolution Schemes [article]

Chandra Chekuri, Jan Vondrák, Rico Zenklusen
2014 arXiv   pre-print
Our algorithms are based on (approximately) maximizing the multilinear extension F of f over a polytope P that represents the constraints, and then effectively rounding the fractional solution.  ...  Our results provide a broadly applicable framework for maximizing linear and submodular functions subject to independence constraints. We give several illustrative examples.  ...  Acknowledgments: We thank Mohit Singh for helpful discussions on contention resolution schemes for matroids, and Shipra Agrawal for discussions concerning the correlation gap.  ... 
arXiv:1105.4593v5 fatcat:msaig7ryozd7nn65ww2dkbutam

Approximation Algorithms for Non-single-minded Profit-Maximization Problems with Limited Supply [chapter]

Khaled Elbassioni, Mahmoud Fouz, Chaitanya Swamy
2010 Lecture Notes in Computer Science  
trees.  ...  For subadditive valuations (and hence submodular, XOS valuations), we obtain a solution with profit OPT SWM /O(log cmax), where OPT SWM is the optimum social welfare and cmax is the maximum item-supply  ...  Our algorithm is a generalization of the one proposed by [6] for unsplittable flow on a line. Root the tree at an arbitrary node.  ... 
doi:10.1007/978-3-642-17572-5_39 fatcat:aa6faftvyzh6lgz5c2kp76pjhq
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