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In this paper we consider several facility location problems with applications to cost and social welfare optimization, when the area map is encoded as a binary (0,1) mxn matrix. We present algorithmic solutions for all the problems. Some cases are too particular to be used in practical situations, but they are at least a starting point for more generic solutions.
We study the multistage $K$-facility reallocation problem on the real line, where we maintain $K$ facility locations over $T$ stages, based on the stage-dependent locations of $n$ agents. Each agent is connected to the nearest facility at each stage,
The restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current best algo
The following online bin packing problem is considered: Items with integer sizes are given and variable sized bins arrive online. A bin must be used if there is still an item remaining which fits in it when the bin arrives. The goal is to minimize th
In this paper, we study the two-facility location game on a line with optional preference where the acceptable set of facilities for each agent could be different and an agents cost is his distance to the closest facility within his acceptable set. T
We study the problem of online graph exploration on undirected graphs, where a searcher has to visit every vertex and return to the origin. Once a new vertex is visited, the searcher learns of all neighboring vertices and the connecting edge weights.