We survey algorithms and hardness results for two important classes of topology optimization problems: computing minimum-weight cycles in a given homotopy or homology class, and computing minimum-weight cycle bases for the fundamental group or various homology groups.

Aerospace applications and energy-saving strategies in general raised the interest and study in the field of lightweight materials, especially on aluminum alloys. Aluminum alloy itself does not have appropriate wear resistance. Therefore, improvement of surface properties is required in practical applications, especially when aluminum is in contact with other parts. In this work, first titanium...

The three dimensional circuit (3D-IC) brings forth new challenges to physical design such as allocation and management of through-silicon-vias (TSVs). Meanwhile, the thermal issues in 3D-IC becomes significant necessitating the use of active cooling schemes such as micro-channel liquid coolings. Both TSVs and micro-channels go through the interlayer regions of 3D-IC resulting in potential resou...

We consider the unit-demand envy-free pricing problem, which is a unit-demand auction where each bidder receives an item that maximizes his utility, and the goal is to maximize the auctioneer’s profit. This problem is NP-hard and unlikely to be in APX. We present four new MIP formulations for it and experimentally compare them to a previous one due to Shioda, Tunçel, and Myklebust. We describe ...

We consider the problem of selecting a subset of alternatives given noisy evaluations of the relative strength of different alternatives. We wish to select a k-subset (for a given k) that provides a maximum likelihood estimate for one of several objectives, e.g., containing the strongest alternative. Although this problem is NP-hard, we show that when the noise level is sufficiently high, intui...

Composite materials using natural rubber as the main matrix are popular these days because of wide applications in modern industries. Rubber also have damping properties, energy absorption, and exposure to continuous loads different environmental conditions. In this research, effect temperatures on rubber-epoxy composite with ratios (0%, 10%, 20%, 30%, 40%, 50%) epoxy has been studied. Where co...