An on-line graph coloring algorithm with sublinear performance ratio
Discrete Mathematics
Lower bounds for on-line graph coloring
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Theoretical Computer Science
Online set packing and competitive scheduling of multi-part tasks
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Streaming algorithms for independent sets
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Online selection of intervals and t-intervals
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Online selection of intervals and t-intervals
Information and Computation
| Hi-index | 5.23 |
We study the online version of the independent set problem in graphs. The vertices of an input graph are given one by one along with their edges to previous vertices, and the task is to decide whether to add each given vertex to an independent set solution. The goal is to maximize the size of the independent set, relative to the size of the optimal independent set. Since it is known that no online algorithm can attain competitive ratio better than n - 1, where n denotes the number of vertices, we study here relaxations where the algorithm can hedge its bets by maintaining multiple alternative solutions.We introduce two models. In the first model, the algorithm can maintain a multiple number (r(n)) of solutions (independent sets) and choose the largest one as the final solution. We show that the best competitive ratio for this model is θ(n/logn) when r(n) is a polynomial and θ(n) when r(n) is a constant. In the second more powerful model, the algorithm can copy intermediate solutions and extend the copied solutions in different ways. We obtain an upper bound O(n/logn) and a lower bound Ω(n/log3n) for the best possible competitive ratio when r(n) is a polynomial. Furthermore, we show a tight θ(n) bound when r(n) is a constant. Lower bound results of this paper hold also for randomized online algorithms against an oblivious adversary.