Sensitivity Analysis for Convex Separable Optimization over Integral Polymatroids

We study the sensitivity of optimal solutions of convex separable optimization problems over an integral polymatroid base polytope with respect to parameters determining both the cost of each eleme...

[1]  Berthold Vöcking,et al.  Nash equilibria and improvement dynamics in congestion games , 2009 .

[2]  Tim Roughgarden,et al.  Network Design with Weighted Players , 2006, SPAA '06.

[3]  K. Murota Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10 , 2003 .

[4]  Awi Federgruen,et al.  The Greedy Procedure for Resource Allocation Problems: Necessary and Sufficient Conditions for Optimality , 1986, Oper. Res..

[5]  Yi Gai,et al.  A packet dropping mechanism for efficient operation of M/M/1 queues with selfish users , 2011, Comput. Networks.

[6]  Peter Sanders,et al.  Scheduling and Traffic Allocation for Tasks with Bounded Splittability , 2003, MFCS.

[7]  Robert W. Rosenthal,et al.  The network equilibrium problem in integers , 1973, Networks.

[8]  Kazuo Murota,et al.  Proximity theorems of discrete convex functions , 2004, Math. Program..

[9]  Berthold Vöcking,et al.  Pure Nash equilibria in player-specific and weighted congestion games , 2006, Theor. Comput. Sci..

[10]  Paul G. Spirakis,et al.  Selfish unsplittable flows , 2005, Theor. Comput. Sci..

[11]  Archie C. Chapman,et al.  On the Existence of Pure Strategy Nash Equilibria in Integer-Splittable Weighted Congestion Games , 2011, SAGT.

[12]  Tim Roughgarden,et al.  The price of stability for network design with fair cost allocation , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[13]  Tim Roughgarden,et al.  Designing Network Protocols for Good Equilibria , 2010, SIAM J. Comput..

[14]  Brigitte Maier,et al.  Supermodularity And Complementarity , 2016 .

[15]  Michel X. Goemans,et al.  Matroids Are Immune to Braess' Paradox , 2015, Math. Oper. Res..

[16]  Yoav Shoham,et al.  Fast and Compact: A Simple Class of Congestion Games , 2005, AAAI.

[17]  Berthold Vöcking,et al.  Pure Nash equilibria in player-specific and weighted congestion games , 2009, Theor. Comput. Sci..

[18]  J. George Shanthikumar,et al.  Convex separable optimization is not much harder than linear optimization , 1990, JACM.

[19]  Andreas S. Schulz,et al.  Network flow problems and congestion games: complexity and approximation results , 2006 .

[20]  Tobias Harks,et al.  Optimal Cost Sharing for Resource Selection Games , 2013, Math. Oper. Res..

[21]  Martin Gairing,et al.  Routing (Un-) Splittable Flow in Games with Player-Specific Linear Latency Functions , 2006, ICALP.

[22]  Nobuyuki Tsuchimura,et al.  M-Convex Function Minimization by Continuous Relaxation Approach: Proximity Theorem and Algorithm , 2011, SIAM J. Optim..

[23]  Max Klimm,et al.  Resource Competition on Integral Polymatroids , 2014, WINE.

[24]  Ross Baldick Refined proximity and sensitivity results in linearly constrained convex separable integer programming , 1995 .

[25]  William J. Cook,et al.  Sensitivity theorems in integer linear programming , 1986, Math. Program..

[26]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[27]  David D. Yao,et al.  Dynamic Scheduling via Polymatroid Optimization , 2002, Performance.

[28]  Spyridon Antonakopoulos,et al.  Buy-at-Bulk Network Design with Protection , 2011, Math. Oper. Res..

[29]  Tim Roughgarden,et al.  The Price of Stability for Network Design with Fair Cost Allocation , 2004, FOCS.

[30]  Vahab S. Mirrokni,et al.  Sink equilibria and convergence , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[31]  H. Groenevelt Two algorithms for maximizing a separable concave function over a polymatroid feasible region , 1991 .

[32]  Max Klimm,et al.  Congestion Games with Player-Specific Costs Revisited , 2013, SAGT.

[33]  Max Klimm,et al.  On the Existence of Pure Nash Equilibria in Weighted Congestion Games , 2010, Math. Oper. Res..

[34]  I. Milchtaich,et al.  Congestion Games with Player-Specific Payoff Functions , 1996 .

[35]  R. Rosenthal A class of games possessing pure-strategy Nash equilibria , 1973 .

[36]  Donald M. Topkis,et al.  Minimizing a Submodular Function on a Lattice , 1978, Oper. Res..

[37]  John N. Tsitsiklis,et al.  A scalable network resource allocation mechanism with bounded efficiency loss , 2006, IEEE Journal on Selected Areas in Communications.

[38]  Tim Roughgarden,et al.  Selfish routing and the price of anarchy , 2005 .

[39]  Max Klimm,et al.  Congestion games with variable demands , 2010, TARK XIII.

[40]  Alain Haurie,et al.  On the relationship between Nash - Cournot and Wardrop equilibria , 1983, Networks.

[41]  Igal Milchtaich,et al.  The Equilibrium Existence Problem in Finite Network Congestion Games , 2006, WINE.

[42]  Aurel A. Lazar,et al.  On the existence of equilibria in noncooperative optimal flow control , 1995, JACM.

[43]  Jiawei Zhang,et al.  Polymatroid Optimization, Submodularity, and Joint Replenishment Games , 2012, Oper. Res..

[44]  Andreas S. Schulz,et al.  On the Complexity of Pure-Strategy Nash Equilibria in Congestion and Local-Effect Games , 2008, Math. Oper. Res..

[45]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[46]  Harold N. Gabow A matroid approach to finding edge connectivity and packing arborescences , 1991, STOC '91.

[47]  Andreas S. Schulz,et al.  On the Complexity of Pure-Strategy Nash Equilibria in Congestion and Local-Effect Games , 2006, WINE.

[48]  Rayadurgam Srikant,et al.  The Mathematics of Internet Congestion Control , 2003 .

[49]  藤重 悟 Submodular functions and optimization , 1991 .