1. 15th Scandinavian Workshop on Algorithm Theory
Algorithms
15th Scandinavian Workshop on Algorithm Theory
June , 2016 in Reykjavik, Iceland

2. Summary
Forum for researchers in the area of design and analysis of algorithms and data structures
Accepted and presented 30 papers
Topics: Approximation algorithms, Graph algorithms, Sets, Strings, Streams, Hard Problems, Online algorithms, Sorting, Scheduling, Games and Geometry.

3. This problem is NP – hard. Previous technique for solving this problem
Coloring Graphs having Few Colorings over Path Decompositions
Coloring graph with different color on every vertex with limited number of k – colors is one famous problem with many applications in real world, for example model resource allocation.
This problem is NP – hard.
Previous technique for solving this problem
Finding the maximum degree of a graph and then greedily coloring the vertices in arbitrary order. But this is also NP – hard.

4. Coloring Graphs having Few Colorings over Path Decompositions
When the author shows that there is a better algorithm (where k is the number of colors and delta is maximum degree of a graph)
But, this is fast only for small k – colorings, if k – coloring is large then the algorithm is getting slower because there are more solutions.
The strategy in the algorithm is that it computes fixed linear combination of all solutions and check if the result is non-zero.
This solution is also in NP - hard class, but authors expect it to run in exponential time for small enough k.

5. Goal is to minimize the number of total comparison operations.
Randomized algorithms for finding a majority element
We are given n colored balls, and we want to detect if more than half are of the same color.
Constraint is that only allowed operation is to choose two balls and compare their colors
Goal is to minimize the number of total comparison operations.
The question is how many comparisons will be made in the worst case.
Previously is proved that comparisons are needed in worst case.

6. They use randomized algorithms to solve this problem
Randomized algorithms for finding a majority element
They use randomized algorithms to solve this problem
Algorithm always finds majority element in a list if it exists.
Or, if there is no such element which occurs more than times algorithm returns none.
Needed comparisons are with high probability

7. Total stability in stable matching games
Problem belongs to the area of matching under preferences.
Goal is to find stable matching
Also seen as a game where each player wants to obtain the best possible partner by manipulating his/her preference list.
Blocking pairs occur which lower the stability

8. Total stability in stable matching games
All valid matching should not include any “blocking pair”
They study the complexity of testing the total stability
Authors show that total stability can be tested in polynomial time
P – a true strategy
Q – an arbitrary stated strategy
They extend this polynomially solvable class to the general one where P and Q may be different