On the Advice Complexity of the Online L(2,1)-Coloring Problem on Paths and Cycles

Bianchi, Maria Paola; Böckenhauer, Hans-Joachim; Hromkovič, Juraj; Krug, Sacha; Steffen, Björn

doi:10.1007/978-3-642-38768-5_7

Cited by 11 publications

(28 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We refer to this model as advice-on-tape model. Since its introduction, the advice-on-tape model has been used to analyze the advice complexity of many online problems including paging [12,26,29], disjoint path allocation [12], job shop scheduling [12,29], k-server [11,30], knapsack [9], various coloring problems [5,21,7,32], set cover [28,10], maximum clique [10], and graph exploration [17].…”

Section: Modelmentioning

confidence: 99%

See 1 more Smart Citation

Online Bin Packing with Advice

et al. 2014

View full text Add to dashboard Cite

We consider the online bin packing problem under the advice complexity model where the "online constraint" is relaxed and an algorithm receives partial information about the future items. We provide tight upper and lower bounds for the amount of advice an algorithm needs to achieve an optimal packing. We also introduce an algorithm that, when provided with log n+o(log n) bits of advice, achieves a competitive ratio of 3/2 for the general problem. This algorithm is simple and is expected to find real-world applications. We introduce another algorithm that receives 2n + o(n) bits of advice and achieves a competitive ratio of 4/3 + ε. Finally, we provide a lower bound argument that implies that advice of linear size is required for an algorithm to achieve a competitive ratio better than 9/8.

show abstract

Section: Modelmentioning

confidence: 99%

“…Provided with the appropriate advice, the online algorithms are expected to achieve improved competitive ratios. The advice model has received significant attention since its introduction [12,26,19,11,29,30,9,6,17,21,28,10,7,32].…”

Section: Introductionmentioning

confidence: 99%

Online Bin Packing with Advice

et al. 2014

View full text Add to dashboard Cite

show abstract

“…Thus, all algorithms achieve the same competitive ratio on instances with idle periods according to (4). Using (1) and the fact that x 0 = 0, we get CR(A 2 l (I)) ≤…”

Section: Theoremmentioning

confidence: 89%

“…No reasonable algorithm ever wakes up on an idle request. 4 On the other hand, the algorithm knows that there is always an idle period on the requests r 2 , r 3 , . .…”

Section: Lower Boundsmentioning

confidence: 99%

See 1 more Smart Citation

On Energy-Efficient Computations With Advice

Böckenhauer

Dobson

Krug

et al. 2015

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. Online problems have always played an important role in computer science. Here, not the whole input is known at the beginning, but it is only revealed gradually. These problems frequently occur in practice, and therefore the performance of algorithms for such problems is of great theoretical and practical interest. One such online problem is energy management in electronic devices, e. g., smartphones. As such a device is usually not being used permanently, it is reasonable to change to a lowerenergy state (like hibernation) after a certain idle time. Resuming from hibernation, however, also needs a certain amount of energy; therefore, hibernation should only happen if the idle period is long. Advice complexity is a recent approach for measuring the information content of an online problem, i. e., the amount of knowledge about the future parts of the input that is necessary to compute a high-quality solution. The approach allows for a more fine-grained analysis of the hardness of online problems than the classical competitive analysis. We analyze the advice complexity of this problem. For systems with two states, we construct an online algorithm with advice that is 1.8-competitive with one advice bit and 1.6-competitive with five advice bits, whereas every deterministic algorithm without advice is known to be no better than 2-competitive. Moreover, the algorithm's competitive ratio converges fast towards e/(e − 1) with an increasing number of advice bits. For competitive ratios in the range [1, e/(e − 1)], we present two complementary algorithms: one behaves optimally on a certain prefix, and the other falls asleep on the longest phases. Conversely, we show that every algorithm with a competitive ratio less than 1 + 1/(4w + 2), where w is the wake-up energy, needs to read a linear number of advice bits.

show abstract

On the Power of Advice and Randomization for the Disjoint Path Allocation Problem

Barhum

Böckenhauer

Forišek

et al. 2014

SOFSEM 2014: Theory and Practice of Computer Science

Self Cite

View full text Add to dashboard Cite

In the disjoint path allocation problem, we consider a path of L + 1 vertices, representing the nodes in a communication network. Requests for an unbounded-time communication between pairs of vertices arrive in an online fashion and a central authority has to decide which of these calls to admit. The constraint is that each edge in the path can serve only one call and the goal is to admit as many calls as possible. Advice complexity is a recently introduced method for a fine-grained analysis of the hardness of online problems. We consider the advice complexity of disjoint path allocation, measured in the length L of the path. We show that asking for a bit of advice for every edge is necessary to be optimal and give online algorithms with advice achieving a constant competitive ratio using much less advice. Furthermore, we consider the case of using less than log log L advice bits, where we prove almost matching lower and upper bounds on the competitive ratio. In the latter case, we moreover show that randomness is as powerful as advice by designing a barely random online algorithm achieving almost the same competitive ratio.

show abstract

On the Advice Complexity of the Online L(2,1)-Coloring Problem on Paths and Cycles

Cited by 11 publications

References 21 publications

Online Bin Packing with Advice

Online Bin Packing with Advice

On Energy-Efficient Computations With Advice

On the Power of Advice and Randomization for the Disjoint Path Allocation Problem

Contact Info

Product

Resources

About