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- research-articleJune 2022
Flow time scheduling and prefix Beck-Fiala
STOC 2022: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of ComputingJune 2022, Pages 331–342https://doi.org/10.1145/3519935.3520077We relate discrepancy theory with the classic scheduling problems of minimizing max flow time and total flow time on unrelated machines. Specifically, we give a general reduction that allows us to transfer discrepancy bounds in the prefix Beck-Fiala (...
- research-articleJune 2021
The metric relaxation for 0-extension admits an Ω(log2/3k) gap
STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of ComputingJune 2021, Pages 1601–1614https://doi.org/10.1145/3406325.3451071We consider the 0-Extension problem, where we are given an undirected graph G=(V,E) equipped with non-negative edge weights w:E→ ℝ+, a collection T={ t1,…,tk}⊆ V of k special vertices called terminals, and a semi-metric D over T. The goal is to assign ...
- research-articleJune 2019
The Salesman’s Improved Paths through Forests
Journal of the ACM (JACM), Volume 66, Issue 4Article No.: 28, Pages 1–16https://doi.org/10.1145/3326123We give a new, strongly polynomial-time algorithm and improved analysis for the metric s-t path Traveling Salesman Problem (TSP). It finds a tour of cost less than 1.53 times the optimum of the subtour elimination linear program (LP), while known ...
- research-articleJuly 2017
From weak to strong LP gaps for all CSPs
CCC '17: Proceedings of the 32nd Computational Complexity ConferenceJuly 2017, Article No.: 11, Pages 1–27We study the approximability of constraint satisfaction problems (CSPs) by linear programming (LP) relaxations. We show that for every CSP, the approximation obtained by a basic LP relaxation, is no weaker than the approximation obtained using ...
- research-articleJanuary 2017
On the configuration-LP of the restricted assignment problem
SODA '17: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete AlgorithmsJanuary 2017, Pages 2670–2678We consider the classical problem of Scheduling on Unrelated Machines. In this problem a set of jobs is to be distributed among a set of machines and the maximum load (makespan) is to be minimized. The processing time pij of a job j depends on the ...
- research-articleJune 2016
Candidate hard unique game
STOC '16: Proceedings of the forty-eighth annual ACM symposium on Theory of ComputingJune 2016, Pages 63–76https://doi.org/10.1145/2897518.2897531We propose a candidate reduction for ruling out polynomial-time algorithms for unique games, either under plausible complexity assumptions, or unconditionally for Lasserre semi-definite programs with a constant number of rounds. We analyze the ...
- research-articleJune 2015
Coalition Games on Interaction Graphs: A Horticultural Perspective
EC '15: Proceedings of the Sixteenth ACM Conference on Economics and ComputationJune 2015, Pages 95–112https://doi.org/10.1145/2764468.2764477We examine cooperative games where the viability of a coalition is determined by whether or not its members have the ability to communicate amongst themselves independently of non-members. This necessary condition for viability was proposed by Myerson [...
- research-articleMarch 2015
The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative-Type Metrics into ℓ1
Journal of the ACM (JACM), Volume 62, Issue 1Article No.: 8, Pages 1–39https://doi.org/10.1145/2629614In this article, we disprove a conjecture of Goemans and Linial; namely, that every negative type metric embeds into ℓ1 with constant distortion. We show that for an arbitrarily small constant δ > 0, for all large enough n, there is an n-point negative ...
- research-articleJanuary 2015
Separation between Estimation and Approximation
ITCS '15: Proceedings of the 2015 Conference on Innovations in Theoretical Computer ScienceJanuary 2015, Pages 271–276https://doi.org/10.1145/2688073.2688101We show (under standard assumptions) that there are \textsf{NP} optimization problems for which estimation is easier than approximation. Namely, one can estimate the value of the optimal solution within a ratio of $\rho$, but it is difficult to find a ...
- research-articleJune 2011
Near-optimal distortion bounds for embedding doubling spaces into L1
STOC '11: Proceedings of the forty-third annual ACM symposium on Theory of computingJune 2011, Pages 765–772https://doi.org/10.1145/1993636.1993737We exhibit an infinite doubling metric space (X,d) such that for any non-expansive f : X -> L1, there exists a pair x,y ∈ X with d(x,y) arbitrarily large, and such that |f(x)-f(y)\|1/d(x,y) ≲ √log log d(x,y)}/(log d(x,y)).
As a consequence, we show that ...
- research-articleJanuary 2011
Sparsest cut on quotients of the hypercube
CATS 2011: Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119January 2011, Pages 11–22We present a simple construction and analysis of an Ω(log log N) integrality gap for the well-known Sparsest Cut semi-definite program (SDP). This holds for the uniform demands version (i.e. edge expansion). The same quantitative gap was proved earlier ...
- research-articleJanuary 2011
Sparsest cut on quotients of the hypercube
CATS '11: Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119January 2011, Pages 11–22We present a simple construction and analysis of an Ω(log log N) integrality gap for the well-known Sparsest Cut semi-definite program (SDP). This holds for the uniform demands version (i.e. edge expansion). The same quantitative gap was proved earlier ...
- research-articleMay 2009
Sherali-adams relaxations of the matching polytope
STOC '09: Proceedings of the forty-first annual ACM symposium on Theory of computingMay 2009, Pages 293–302https://doi.org/10.1145/1536414.1536456We study the Sherali-Adams lift-and-project hierarchy of linear programming relaxations of the matching polytope. Our main result is an asymptotically tight expression 1+1/k for the integrality gap after k rounds of this hierarchy. The result is derived ...
- articleNovember 2007
Approximation algorithms and hardness results for cycle packing problems
ACM Transactions on Algorithms (TALG), Volume 3, Issue 4Pages 48–eshttps://doi.org/10.1145/1290672.1290685The cycle packing number νe(G) of a graph G is the maximum number of pairwise edge-disjoint cycles in G. Computing νe(G) is an NP-hard problem. We present approximation algorithms for computing νe(G) in both undirected and directed graphs. In the ...
- articleAugust 2007
Multicommodity demand flow in a tree and packing integer programs
ACM Transactions on Algorithms (TALG), Volume 3, Issue 3Pages 27–eshttps://doi.org/10.1145/1273340.1273343We consider requests for capacity in a given tree network T = (V, E) where each edge e of the tree has some integer capacity ue. Each request f is a node pair with an integer demand df and a profit wf which is obtained if the request is satisfied. The ...
- ArticleJune 2007
Tight integrality gaps for Lovasz-Schrijver LP relaxations of vertex cover and max cut
STOC '07: Proceedings of the thirty-ninth annual ACM symposium on Theory of computingJune 2007, Pages 302–310https://doi.org/10.1145/1250790.1250836We study linear programming relaxations of Vertex Cover and Max Cutarising from repeated applications of the "lift-and-project" method of Lovasz and Schrijver starting from the standard linear programming relaxation.
For Vertex Cover, Arora, Bollobas, ...
- ArticleJune 2007
Hardness of routing with congestion in directed graphs
STOC '07: Proceedings of the thirty-ninth annual ACM symposium on Theory of computingJune 2007, Pages 165–178https://doi.org/10.1145/1250790.1250816Given as input a directed graph on n vertices and a set ofsource-destination pairs, we study the problem of routing themaximum possible number of source-destination pairs on paths, suchthat at most c(N) paths go through any edge. We show that theproblem ...