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- research-articleJanuary 2022
An Improved Approximation Algorithm for The Asymmetric Traveling Salesman Problem
SIAM Journal on Computing (SICOMP), Volume 51, Issue 1Feb 2022, Pages 139–173https://doi.org/10.1137/20M1339313We revisit the constant-factor approximation algorithm for the asymmetric traveling salesman problem by Svensson, Tarnawski, and Végh [J. ACM, 67 (2020), 37]. We improve on each part of this algorithm. We avoid the reduction to irreducible instances and thus ...
- research-articleJanuary 2021
Reducing Path TSP to TSP
SIAM Journal on Computing (SICOMP), Volume 51, Issue 3Jun 2022, Pages STOC20-24–STOC20-53https://doi.org/10.1137/20M135594XWe present a black-box reduction from the path version of the traveling salesman problem (Path TSP) to the classical tour version (TSP). More precisely, given an $\alpha$-approximation algorithm for TSP, then, for any $\epsilon >0$, we obtain an $(\alpha+\...
- research-articleJanuary 2020
Fair Scheduling via Iterative Quasi-Uniform Sampling
SIAM Journal on Computing (SICOMP), Volume 49, Issue 32020, Pages 658–680https://doi.org/10.1137/18M1202451This paper considers minimizing the $\ell_k$-norms of flow time on a single machine offline using a preemptive scheduler for $k\geq 1$. The objective is ideal for optimizing jobs' overall waiting times while simultaneously being fair to individual jobs. ...
- research-articleJanuary 2020
Scheduling to Minimize Total Weighted Completion Time via Time-Indexed Linear Programming Relaxations
SIAM Journal on Computing (SICOMP), Volume 49, Issue 42020, Pages FOCS17-409–FOCS17-440https://doi.org/10.1137/17M1156332We study approximation algorithms for problems of scheduling precedence constrained jobs with the objective of minimizing total weighted completion time, in identical and related machine models. We give algorithms that improve upon many previous 15- to 20-...
- research-articleJanuary 2020
New Hardness Results for Routing on Disjoint Paths
SIAM Journal on Computing (SICOMP), Volume 51, Issue 2Apr 2022, Pages STOC17-189–STOC17-237https://doi.org/10.1137/17M1146580In the classical node-disjoint paths (\sf NDP) problem, the input consists of an undirected $n$-vertex graph $G$, and a collection ${\mathcal M}=\{(s_1,t_1),\ldots,(s_k,t_k)\}$ of pairs of its vertices, called source-destination, or demand pairs. The goal ...
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- research-articleJanuary 2020
Bidimensionality and Kernels
SIAM Journal on Computing (SICOMP), Volume 49, Issue 62020, Pages 1397–1422https://doi.org/10.1137/16M1080264Bidimensionality theory was introduced by [E. D. Demaine et al., J. ACM, 52 (2005), pp. 866--893] as a tool to obtain subexponential time parameterized algorithms on H-minor-free graphs. In [E. D. Demaine and M. Hajiaghayi, Bidimensionality: New ...
- research-articleJanuary 2019
Inapproximability of the Independent Set Polynomial in the Complex Plane
SIAM Journal on Computing (SICOMP), Volume 49, Issue 52020, Pages STOC18-395–STOC18-448https://doi.org/10.1137/18M1184485We study the complexity of approximating the value of the independent set polynomial $Z_G(\lambda)$ of a graph $G$ with maximum degree $\Delta$ when the activity $\lambda$ is a complex number. When $\lambda$ is real, the complexity picture is well ...
- research-articleJanuary 2019
Local Search Yields Approximation Schemes for $k$-Means and $k$-Median in Euclidean and Minor-Free Metrics
SIAM Journal on Computing (SICOMP), Volume 48, Issue 22019, Pages 644–667https://doi.org/10.1137/17M112717XWe give the first polynomial-time approximation schemes (PTASs) for the following problems: (1) uniform facility location in edge-weighted planar graphs; (2) $k$-median and $k$-means in edge-weighted planar graphs; and (3) $k$-means in Euclidean space of ...
- research-articleJanuary 2019
Better Guarantees for $k$-Means and Euclidean $k$-Median by Primal-Dual Algorithms
SIAM Journal on Computing (SICOMP), Volume 49, Issue 42020, Pages FOCS17-97–FOCS17-156https://doi.org/10.1137/18M1171321Clustering is a classic topic in optimization with $k$-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best-known algorithm for $k$-means in Euclidean space with a provable guarantee is a simple ...
- research-articleJanuary 2018
Online Buy-at-Bulk Network Design
SIAM Journal on Computing (SICOMP), Volume 47, Issue 42018, Pages 1505–1528https://doi.org/10.1137/16M1117317We present the first online algorithms for the nonuniform, multicommodity buy-at-bulk (MC-BB) network design problem. Our competitive ratios qualitatively match the best known approximation factors for the corresponding offline problems. In particular, we ...
- research-articleJanuary 2018
Approximation Algorithms for Euler Genus and Related Problems
SIAM Journal on Computing (SICOMP), Volume 47, Issue 42018, Pages 1610–1643https://doi.org/10.1137/14099228XThe Euler genus of a graph is a fundamental and well-studied parameter in graph theory and topology. Computing it has been shown to be NP-hard by Thomassen [J. Algorithms, 10 (1989), pp. 568--576; J. Combin. Theory, Ser. B, 57 (1993), pp. 196--206], and it is ...
- research-articleJanuary 2018
All-or-Nothing Multicommodity Flow Problem with Bounded Fractionality in Planar Graphs
SIAM Journal on Computing (SICOMP), Volume 47, Issue 42018, Pages 1483–1504https://doi.org/10.1137/130932326We study the following all-or-nothing multicommodity flow problem in planar graphs: Input: A graph $G$ with $n$ vertices and $k$ pairs of vertices $(s_1,t_1),(s_2,t_2),\dots, (s_k,t_k)$ in $G$. Find: A largest subset $W$ of $\{1,\dots,k\}$ such that for ...
- research-articleJanuary 2018
Primal Beats Dual on Online Packing LPs in the Random-Order Model
SIAM Journal on Computing (SICOMP), Volume 47, Issue 52018, Pages 1939–1964https://doi.org/10.1137/15M1033708We study packing linear programs (LPs) in an online model where the columns are presented to the algorithm in random order. This natural problem was investigated in various recent studies motivated, e.g., by online ad allocations and yield management, ...
- research-articleJanuary 2017
Deterministic Polynomial-Time Approximation Algorithms for Partition Functions and Graph Polynomials
SIAM Journal on Computing (SICOMP), Volume 46, Issue 62017, Pages 1893–1919https://doi.org/10.1137/16M1101003In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In particular, our approach works for the Tutte ...
- research-articleJanuary 2017
Approximately Counting Triangles in Sublinear Time
SIAM Journal on Computing (SICOMP), Volume 46, Issue 52017, Pages 1603–1646https://doi.org/10.1137/15M1054389We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in both theory and practice, but all existing algorithms read the entire graph. In this work we design a sublinear-time algorithm for ...
- research-articleJanuary 2017
LP-Based Algorithms for Capacitated Facility Location
SIAM Journal on Computing (SICOMP), Volume 46, Issue 12017, Pages 272–306https://doi.org/10.1137/151002320Linear programming (LP) has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of algorithmic ...
- research-articleJanuary 2017
Greedy Algorithms for the Maximum Satisfiability Problem: Simple Algorithms and Inapproximability Bounds
SIAM Journal on Computing (SICOMP), Volume 46, Issue 32017, Pages 1029–1061https://doi.org/10.1137/15M1053369We give a simple, randomized greedy algorithm for the maximum satisfiability problem (MAX SAT) that obtains a $\frac{3}{4}$-approximation in expectation. In contrast to previously known $\frac{3}{4}$-approximation algorithms, our algorithm does not use flows ...
- research-articleJanuary 2017
Estimating the Longest Increasing Sequence in Polylogarithmic Time
SIAM Journal on Computing (SICOMP), Volume 46, Issue 22017, Pages 774–823https://doi.org/10.1137/130942152Finding the length of the longest increasing subsequence (LIS) is a classic algorithmic problem. Let $n$ denote the size of the array. Simple $O(n\log n)$ algorithms are known for this problem. We develop a polylogarithmic time randomized algorithm that for ...
- research-articleJanuary 2016
Special Section on the Fifty-Fifth Annual ACM Symposium on Foundations of Coomputer Science (FOCS 2014)
SIAM Journal on Computing (SICOMP), Volume 46, Issue 12017, Page 160https://doi.org/10.1137/16N974309This special section comprises ten fully refereed papers whose extended abstracts were presented at the 55th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2014) in Philadelphia, Pennsylvania, October 19--21, 2014. The unrefereed conference ...
- research-articleJanuary 2016
Dynamic Approximate All-Pairs Shortest Paths: Breaking the $O(mn)$ Barrier and Derandomization
SIAM Journal on Computing (SICOMP), Volume 45, Issue 32016, Pages 947–1006https://doi.org/10.1137/140957299We study dynamic $(1+\epsilon)$-approximation algorithms for the all-pairs shortest paths problem in unweighted undirected $n$-node $m$-edge graphs under edge deletions. The fastest algorithm for this problem is a randomized algorithm with a total update ...