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J Hȧstad (1999)
Clique is hard to approximate within $$n^{1-\epsilon }$$ n 1 - ϵActa Math., 182
C Chekuri, S Khanna (2005)
A polynomial time approximation scheme for the multiple knapsack problemSIAM J. Comput., 35
M Dawande, J Kalagnanam, P Keskinocak, FS Salman, R Ravi (2000)
Approximation algorithms for the multiple knapsack problem with assignment restrictionsJ. Comb. Optim., 4
AM Frieze, MRB Clarke (1984)
Approximation algorithms for the $$m$$ m -dimensional $$0-1$$ 0 - 1 knapsack problem: worst-case and probabilistic analysesEur. J. Oper. Res., 15
S Sahni (1975)
Approximate algorithms for the 0/1 knapsack problemJ. ACM, 22
D Amzallag, R Bar-Yehuda, D Raz, G Scalosub (2013)
Cell selection in 4G cellular networksIEEE Trans. Mobile Comput., 12
R Bar-Yehuda, S Even (1985)
A local-ratio theorem for approximating the weighted vertex cover problemAnn. Discret. Math., 25
E Hazan, S Safra, O Schwartz (2006)
On the complexity of approximating $$k$$ k -set packingComput. Complex., 15
Y Emek, MM Halldórsson, Y Mansour, B Patt-Shamir, J Radhakrishnan, D Rawitz (2012)
Online set packingSIAM J. Comput., 41
P Erdös, A Hajnal (1966)
On chromatic number of graphs and set-systemsActa Math. Hung., 17
R Bar-Yehuda, K Bendel, A Freund, D Rawitz (2004)
Local ratio: a unified framework for approximation algorithmsACM Comput. Surv., 36
C Chekuri, S Khanna (2004)
On multidimensional packing problemsSIAM J. Comput., 33
M Luby (1986)
A simple parallel algorithm for the maximal independent set problemSIAM J. Comput., 15
B Awerbuch (1985)
Complexity of network synchronizationJ. ACM, 32
OH Ibarra, CE Kim (1975)
Fast approximation algorithms for the knapsack and sum of subset problemsJ. ACM, 22
A Srinivasan (1999)
Improved approximation guarantees for packing and covering integer programsSIAM J. Comput., 29
R Cohen, G Grebla (2015)
Joint scheduling and fast cell selection in OFDMA wireless networksIEEE/ACM Trans. Netw., 23
A Bar-Noy, R Bar-Yehuda, A Freund, J Naor, B Schieber (2001)
A unified approach to approximating resource allocation and schedulingJ. ACM, 48
R Cohen, L Katzir, D Raz (2006)
An efficient approximation for the generalized assignment problemInf. Process. Lett., 100
DB Shmoys, É Tardos (1993)
An approximation algorithm for the generalized assignment problemMath. Program., 62
P Raghavan, CD Thompson (1987)
Randomized rounding: a technique for provably good algorithms and algorithmic proofsCombinatorica, 7
MJ Magazine, MS Chern (1984)
A note on approximation schemes for multidimensional knapsack problemsMath. Oper. Res., 9
B Patt-Shamir, D Rawitz, G Scalosub (2012)
Distributed approximation of cellular coverageJ. Parallel Distrib. Comput., 72
We consider the k-Service Assignment problem ( $$k$$ k -SA). The input consists of a network that contains servers and clients. Associated with each client is a demand and a profit. In addition, each client c has a service requirement[InlineEquation not available: see fulltext.], where $$\kappa (c)$$ κ ( c ) is a positive integer. A client c is satisfied only if its demand is handled by exactly $$\kappa (c)$$ κ ( c ) neighboring servers. The objective is to maximize the total profit of satisfied clients, while obeying the given capacity limits of the servers. We focus here on the more challenging case of hard constraints, where no profit is granted for partially satisfied clients. This models, e.g., when a client wants, for reasons of fault tolerance, a file to be stored at $$\kappa (c)$$ κ ( c ) or more nearby servers. Other motivations from the literature include resource allocation in 4G cellular networks and machine scheduling on related machines with assignment restrictions. In the r-restricted version of $$k$$ k -SA, no client requires more than an r-fraction of the capacity of any adjacent server. We present a (centralized) polynomial-time [InlineEquation not available: see fulltext.]-approximation algorithm for r-restricted $$k$$ k -SA. A variant of this algorithm achieves an approximation ratio of [InlineEquation not available: see fulltext.] when given a resource augmentation factor of $$1+r$$ 1 + r . We use the latter result to present a [InlineEquation not available: see fulltext.]-approximation algorithm for $$k$$ k -SA. In the distributed setting, we present: (i) a [InlineEquation not available: see fulltext.]-approximation algorithm for r-restricted $$k$$ k -SA, (ii) a [InlineEquation not available: see fulltext.]-approximation algorithm that uses a resource augmentation factor of $$1+r$$ 1 + r for r-restricted $$k$$ k -SA, both for any constant $$\varepsilon >0$$ ε > 0 , and (iii) an [InlineEquation not available: see fulltext.]-approximation algorithm for $$k$$ k -SA (in expectation). The three distributed algorithms run in $$O(k^2 \varepsilon ^{-2} \log ^3 n)$$ O ( k 2 ε - 2 log 3 n ) synchronous rounds (with high probability). In particular, this yields the first distributed [InlineEquation not available: see fulltext.]-approximation of $$1$$ 1 -SA.
Distributed Computing – Springer Journals
Published: Dec 30, 2017
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