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- research-articleMarch 2021
On the mysteries of MAX NAE-SAT
SODA '21: Proceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete AlgorithmsPages 484–503MAX NAE-SAT is a natural optimization problem, closely related to its better-known relative MAX SAT. The approximability status of MAX NAE-SAT is almost completely understood if all clauses have the same size k, for some k ≥ 2. We refer to this problem ...
- research-articleJanuary 2019
A sort of an adversary
SODA '19: Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete AlgorithmsPages 1291–1310We describe an efficient deterministic adversary that forces any comparison-based sorting algorithm to perform at least [MATH HERE] n log n comparisons. This improves on previous efficient adversaries of Atallah and Kosaraju (1981), Richards and Vaidya (...
- research-articleJanuary 2015
The amortized cost of finding the minimum
SODA '15: Proceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithmsPages 757–768We obtain an essentially optimal tradeoff between the amortized cost of the three basic priority queue operations insert, delete and find-min in the comparison model. More specifically we show that
[EQUATION]
for any fixed ε > 0, where n is the number ...
- research-articleJanuary 2014
Improved upper bounds for random-edge and random-jump on abstract cubes
SODA '14: Proceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithmsPages 874–881Upper bounds are given for the complexity of two very natural randomized algorithms for finding the sink of an Acyclic Unique Sink Orientation (AUSO) of the n-cube. For Random-Edge, we obtain an upper bound of about 1.80n, improving upon the the ...
- research-articleJanuary 2014
Dantzig's pivoting rule for shortest paths, deterministic MDPs, and minimum cost to time ratio cycles
SODA '14: Proceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithmsPages 847–860Dantzig's pivoting rule is one of the most studied pivoting rules for the simplex algorithm. While the simplex algorithm with Dantzig's rule may require an exponential number of pivoting steps on general linear programs, and even on min cost flow ...
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- research-articleJanuary 2011
Collapse
SODA '11: Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithmsPages 603–613The problem of checking whether a given tower of bricks is stable can be easily answered by checking whether a system of linear inequalities has a feasible solution. A more challenging problem is to determine how an unstable tower of bricks collapses. ...
- research-articleJanuary 2011
A subexponential lower bound for the random facet algorithm for parity games
SODA '11: Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithmsPages 202–216Parity Games form an intriguing family of infinite duration games whose solution is equivalent to the solution of important problems in automatic verification and automata theory. They also form a very natural subclass of Deterministic Mean Payoff Games,...
- research-articleJanuary 2009
Discounted deterministic Markov decision processes and discounted all-pairs shortest paths
SODA '09: Proceedings of the twentieth annual ACM-SIAM symposium on Discrete algorithmsPages 958–967We present two new algorithms for finding optimal strategies for discounted, infinite-horizon, Deterministic Markov Decision Processes (DMDP). The first one is an adaptation of an algorithm of Young, Tarjan and Orlin for finding minimum mean weight ...
- research-articleJanuary 2009
A simpler implementation and analysis of Chazelle's soft heaps
SODA '09: Proceedings of the twentieth annual ACM-SIAM symposium on Discrete algorithmsPages 477–485Chazelle (JACM 47(6), 2000) devised an approximate meldable priority queue data structure, called Soft Heaps, and used it to obtain the fastest known deterministic comparison-based algorithm for computing minimum spanning trees, as well as some new ...
- research-articleJanuary 2009
Efficient algorithms for the 2-gathering problem
Pebbles are placed on some vertices of a directed graph. Is it possible to move each pebble along at most one edge of the graph so that in the final configuration no pebble is left on its own? We give an O(mn)-time algorithm for solving this problem, ...
- extended-abstractJanuary 2008
Maximum overhang
SODA '08: Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithmsPages 756–765How far can a stack of n identical blocks be made to hang over the edge of a table? The question dates back to at least the middle of the 19th century and the answer to it was widely believed to be of order log n. However, at SODA'06, Paterson and Zwick ...
- ArticleJanuary 2007
All-pairs bottleneck paths in vertex weighted graphs
SODA '07: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithmsPages 978–985Let G = (V, E, w) be a directed graph, where w : V ← R is an arbitrary weight function defined on its vertices. The bottleneck weight, or the capacity, of a path is the smallest weight of a vertex on the path. For two vertices u, v the bottleneck weight,...
- ArticleJanuary 2007
Deterministic rendezvous, treasure hunts and strongly universal exploration sequences
SODA '07: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithmsPages 599–608We obtain several improved solutions for the deterministic rendezvous problem in general undirected graphs. Our solutions answer several problems left open in a recent paper by Dessmark et al. We also introduce an interesting variant of the rendezvous ...
- ArticleJanuary 2007
Maximum matching in graphs with an excluded minor
SODA '07: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithmsPages 108–117We present a new randomized algorithm for finding a maximum matching in H-minor free graphs. For every fixed H, our algorithm runs in O(n3ω/(ω+3)) < O(n1.326) time, where n is the number of vertices of the input graph and ω < 2.376 is the exponent of ...
- ArticleJanuary 2006
Spanners and emulators with sublinear distance errors
SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithmPages 802–809Let k ≥ 2 be an integer. We show that any undirected and unweighted graph G = (V, E) on n vertices has a subgraph G' = (V, E') with O(kn1+1/k) edges such that for any two vertices u, v ∈ V, if δG(u, v) = d, then δG'(u, v) = d+O(d1-1/k-1). Furthermore, ...
- ArticleJanuary 2006
Overhang
SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithmPages 231–240How far off the edge of the table can we reach by stacking n identical blocks of length 1? A classical solution achieves an overhang of 1/2Hn, where Hn = Σni=1 1/i ~ ln n is the nth harmonic number, by stacking all the blocks one on top of another with ...
- ArticleJanuary 2006
A deterministic subexponential algorithm for solving parity games
SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithmPages 117–123The existence of polynomial time algorithms for the solution of parity games is a major open problem. The fastest known algorithms for the problem are randomized algorithms that run in subexponential time. These algorithms are all ultimately based on ...
- ArticleJanuary 2004
Detecting short directed cycles using rectangular matrix multiplication and dynamic programming
SODA '04: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithmsPages 254–260We present several new algorithms for detecting short fixed length cycles in digraphs. The new algorithms utilize fast rectangular matrix multiplication algorithms together with a dynamic programming approach similar to the one used in the solution of ...
- ArticleJanuary 2004
Meldable RAM priority queues and minimum directed spanning trees
We consider the implementation of meldable priority queues with integer keys in the RAM model. We present two new general techniques for transforming non-meldable priority queues into meldable ones. These transformations can be described symbolically as:...
- ArticleJanuary 2002
Reachability and distance queries via 2-hop labels
SODA '02: Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithmsPages 937–946Reachability and distance queries in graphs are fundamental to numerous applications, ranging from geographic navigation systems to Internet routing. Some of these applications involve huge graphs and yet require fast query answering. We propose a new ...