An O(20.304n) Algorithm for Solving Maximum Independent Set Problem
IEEE Transactions on Computers
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
New methods for 3-SAT decision and worst-case analysis
Theoretical Computer Science
Finding maximum independent sets in sparse and general graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Computing Partitions with Applications to the Knapsack Problem
Journal of the ACM (JACM)
A lower bound for DLL algorithms for k-SAT (preliminary version)
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A machine program for theorem-proving
Communications of the ACM
Vertex cover: further observations and further improvements
Journal of Algorithms
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
SAT Local Search Algorithms: Worst-Case Study
Journal of Automated Reasoning
New Worst-Case Upper Bounds for SAT
Journal of Automated Reasoning
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A generating function approach to the Traveling Salesman Problem
ACM '77 Proceedings of the 1977 annual conference
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Worst-case upper bounds for MAX-2-SAT with an application to MAX-CUT
Discrete Applied Mathematics - The renesse issue on satisfiability
Improved upper bounds for 3-SAT
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Algorithms
An improved deterministic local search algorithm for 3-SAT
Theoretical Computer Science
An improved exponential-time algorithm for k-SAT
Journal of the ACM (JACM)
A new approach to proving upper bounds for MAX-2-SAT
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Measure and conquer: a simple O(20.288n) independent set algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A new algorithm for optimal 2-constraint satisfaction and its implications
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Exponential Lower Bounds for the Running Time of DPLL Algorithms on Satisfiable Formulas
Journal of Automated Reasoning
Inclusion--Exclusion Algorithms for Counting Set Partitions
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
An O*(2^n ) Algorithm for Graph Coloring and Other Partitioning Problems via Inclusion--Exclusion
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Quasiconvex analysis of multivariate recurrence equations for backtracking algorithms
ACM Transactions on Algorithms (TALG)
An improved exact algorithm for the domatic number problem
Information Processing Letters
On exact algorithms for treewidth
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
An exact algorithm for the minimum dominating clique problem
Theoretical Computer Science
Exact Algorithms for Treewidth and Minimum Fill-In
SIAM Journal on Computing
Solving Connected Dominating Set Faster than 2 n
Algorithmica - Parameterized and Exact Algorithms
On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms
Algorithmica - Parameterized and Exact Algorithms
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications
ACM Transactions on Algorithms (TALG)
A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Improved edge-coloring with three colors
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Fast exponential algorithms for maximum γ-regular induced subgraph problems
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Exact computation of maximum induced forest
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Measure and conquer: domination – a case study
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Algorithmics in exponential time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Exact (exponential) algorithms for the dominating set problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
A faster algorithm for finding maximum independent sets in sparse graphs
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Improved exponential-time algorithms for treewidth and minimum fill-in
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Enumerating maximal independent sets with applications to graph colouring
Operations Research Letters
Counting minimum weighted dominating sets
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
An Amortized Search Tree Analysis for k-Leaf Spanning Tree
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Iterative compression and exact algorithms
Theoretical Computer Science
Improved upper bounds for vertex cover
Theoretical Computer Science
A new upper bound for Max-2-SAT: A graph-theoretic approach
Journal of Discrete Algorithms
Breaking the 2n-barrier for Irredundance: Two lines of attack
Journal of Discrete Algorithms
Branch-cut-and-propagate for the maximum k-colorable subgraph problem with symmetry
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Exact algorithms for dominating set
Discrete Applied Mathematics
Enumerating minimal subset feedback vertex sets
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
An exact algorithm for the Maximum Leaf Spanning Tree problem
Theoretical Computer Science
Scheduling partially ordered jobs faster than 2n
ESA'11 Proceedings of the 19th European conference on Algorithms
Capacitated domination faster than O(2n)
Information Processing Letters
ACM Transactions on Algorithms (TALG)
A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between
Journal of Computer and System Sciences
Sharp separation and applications to exact and parameterized algorithms
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Maximum independent set in graphs of average degree at most three in O(1.08537n)
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Bicolored independent sets and bicliques
Information Processing Letters
A bottom-up method and fast algorithms for MAX INDEPENDENT SET
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Capacitated domination faster than O(2n)
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
A faster exact algorithm for the directed maximum leaf spanning tree problem
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Fast algorithms for min independent dominating set
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Polynomial space algorithms for counting dominating sets and the domatic number
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Irredundant set faster than O(2n)
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
A parameterized route to exact puzzles: breaking the 2n-barrier for irredundance (Extended Abstract)
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
An exact exponential time algorithm for counting bipartite cliques
Information Processing Letters
An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problem
Journal of Discrete Algorithms
Solving the 2-disjoint connected subgraphs problem faster than 2n
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Algorithms for dominating clique problems
Theoretical Computer Science
Finding a maximum induced degenerate subgraph faster than 2n
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Efficient algorithms for the max k-vertex cover problem
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
Communications of the ACM
Fast algorithms for min independent dominating set
Discrete Applied Mathematics
Fast exact algorithm for L(2,1)-labeling of graphs
Theoretical Computer Science
Computing the differential of a graph: Hardness, approximability and exact algorithms
Discrete Applied Mathematics
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For more than 40 years, Branch & Reduce exponential-time backtracking algorithms have been among the most common tools used for finding exact solutions of NP-hard problems. Despite that, the way to analyze such recursive algorithms is still far from producing tight worst-case running time bounds. Motivated by this, we use an approach, that we call “Measure & Conquer”, as an attempt to step beyond such limitations. The approach is based on the careful design of a nonstandard measure of the subproblem size; this measure is then used to lower bound the progress made by the algorithm at each branching step. The idea is that a smarter measure may capture behaviors of the algorithm that a standard measure might not be able to exploit, and hence lead to a significantly better worst-case time analysis. In order to show the potentialities of Measure & Conquer, we consider two well-studied NP-hard problems: minimum dominating set and maximum independent set. For the first problem, we consider the current best algorithm, and prove (thanks to a better measure) a much tighter running time bound for it. For the second problem, we describe a new, simple algorithm, and show that its running time is competitive with the current best time bounds, achieved with far more complicated algorithms (and standard analysis). Our examples show that a good choice of the measure, made in the very first stages of exact algorithms design, can have a tremendous impact on the running time bounds achievable.