Scheduling to minimize gaps and power consumption

This paper considers scheduling tasks while minimizing the power consumption of one or more processors, each of which can go to sleep at a fixed cost α . There are two natural versions of this problem, both considered extensively in recent work: minimize the total power consumption (including computation time), or minimize the number of “gaps” in execution. For both versions in a multiprocessor system, we develop a polynomial-time algorithm based on sophisticated dynamic programming. In a generalization of the power-saving problem, where each task can execute in any of a specified set of time intervals, we develop a (1+23α) -approximation, and show that dependence on α is necessary. In contrast, the analogous multi-interval gap scheduling problem is set-cover hard (and thus not o(lgn) -approximable), even in the special cases of just two intervals per job or just three unit intervals per job. We also prove several other hardness-of-approximation results. Finally, we give an O(n√) -approximation for maximizing throughput given a hard upper bound on the number of gaps.Institute for Research in Fundamental Sciences (Iran) (Grant Number CS1385-2-01)Institute for Research in Fundamental Sciences (Iran) (Grant Number CS1384-6-01

An Efficient Local Search for Partial Latin Square Extension Problem

A partial Latin square (PLS) is a partial assignment of n symbols to an nxn grid such that, in each row and in each column, each symbol appears at most once. The partial Latin square extension problem is an NP-hard problem that asks for a largest extension of a given PLS. In this paper we propose an efficient local search for this problem. We focus on the local search such that the neighborhood is defined by (p,q)-swap, i.e., removing exactly p symbols and then assigning symbols to at most q empty cells. For p in {1,2,3}, our neighborhood search algorithm finds an improved solution or concludes that no such solution exists in O(n^{p+1}) time. We also propose a novel swap operation, Trellis-swap, which is a generalization of (1,q)-swap and (2,q)-swap. Our Trellis-neighborhood search algorithm takes O(n^{3.5}) time to do the same thing. Using these neighborhood search algorithms, we design a prototype iterated local search algorithm and show its effectiveness in comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX and LocalSolver.Comment: 17 pages, 2 figure

Benders' decompositie voor statistiek

Use of Benders decomposition for the secondary cell suppression problem, so as to protect sensistive data in publicly available table

An LP-based heuristic for the post enrolment course timetabling problem of the ITC

\u3cp\u3eWe present a deterministic heuristic for the post enrolment course timetabling problem of the ITC. The heuristic is based on an LP-solution constructed with column generation. We get an integer solution by fixing a column one at a time. Our results are compared with the results of the five finalists.\u3c/p\u3

An IP-based heuristic for the post enrolment course timetabling problem of the ITC2007

Track 2 of the international timetabling competition 2007 was a post enrolment course timetabling problem. A set of events has to be assigned to a timeslot and to a room such that all students are able to attend their requested events while not violating the hard constraints. There are also soft constraints that make the timetable nicer . We present a deterministic heuristic that assigns events to timeslots based on an LP-solution constructed with column generation. We get an integer solution by fixing columns one at a time. This heuristic finds a solution that obeys all the hard constraint for 23 of the 24 instances of the competition. The generated solution is improved by selecting a set of events that are reassigned by solving an integer program. This IP minimizes the number of soft constraint violations under the restriction that no hard constraints are violated. Comparing the results of our heuristic with the results of the five finalists of the competition, shows that our approach is competitive

A new heuristic for job shops with no-wait and blocking constraints

Traditional job shop scheduling problems assume that there are buffers with infinite capacity available, which is not always true in the real world. We consider job shop scheduling problems with operations that have to start immediately after their predecessor operation is completed (no-wait precedence constraint) or the resource of the completed operation is not released until the resource of the next operation is released (blocking precedence constraint). An application is the planning of shunting movements in a railway system. A new heuristic and an integer programming formulation for a job shop with precedence constraints that are blocking or no-wait are presented. The heuristics known in literature have the main disadvantage that they do not always find a feasible solution. The heuristic presented here always finds one and tests show that the solutions found are of a good quality

A reversible loss system with multi-type customers and multi-type servers

We consider a memoryless loss system with servers S = {1, ..., J}, and with customer types C = {1, ..., I}. Servers are multi-type, so that server j can serve a subset of customer types C(j). We show that the probabilities of assigning arriving customers to idle servers can be chosen in such a way that the Markov process describing the system is reversible, with a simple product form stationary distribution. Furthermore, the system is insensitive, these properties are preserved for general service time distributions

The Cinderella game on holes and anti-holes

We investigate a two-player game on graphs, where one player (Cinderella) wants to keep the behavior of an underlying water-bucket system stable whereas the other player (the wicked Stepmother) wants to cause overflows. The bucket number of a graph G is the smallest possible bucket size with which Cinderella can win the game. We determine the bucket numbers of all perfect graphs, and we also derive results on the bucket numbers of certain non-perfect graphs. In particular, we analyze the game on holes and (partially) on anti-holes for the cases where Cinderella sticks to a simple greedy strategy